O C/1O>KHOCTH npob/iembl TO>KAECTBA fl/ih KOHEHHO OnPEAE/IEHHblX TPYnn M.K.BA/1HEB

Átírás

1 Anre6pa H normca, 8, Ns 1 (1969), 5. YAK 51.01:518.5: O C/1O>KHOCTH npob/iembl TO>KAECTBA fl/ih KOHEHHO OnPEAE/IEHHblX TPYnn M.K.BA/1HEB KaK H3B6CTHO, anrophtmhieckah HepaapeuiHMOCTfa npo6nembi ctba ana KOHGHHO onpenenehhbix rpynn (x.e. rpynn, aaaahhbix KOHennoft chcxemoii o6paayiomhx H onpeaenflioinhx coothouiehhlt) 6wna yctahobneaa n.c.hobhkobwm C 1 II. IloaflHee B.B.BynoM C2H, F.XHrMaHOM C3D H AK.BPHTTOHOM 114 H SbinH npennomcehbi npyme flokaaarejibctba sroro pe -. Ka»noe as STHX nokaaarenfactb ochobano Ha nekotopojs KOHCT, Koxopaa no niosomy pekypchbho nepeihcrihmomy (Kopone, p.n. ) MHO»ecTBy o CTPOHT KOH6HHO onpeflenehhyro (Kopone, K.O. ) rpynny K, K nposneme TOKflecrBa (Kopoie, n.r.) nna Koropoft a^ekthbho CBOAHTCH nposnema paapeuihmocth zwa S. flanbhefimee HccjieaoaaHHe STHX KOHCT - pyxuhh (4>pHflMaH C5I], KnanxsM C6H, noanaee Byn C73, BoxyTfa L8~A ) no- Kaaano, HTO HMeex Mecro TaK»ce 3(t4ieKTHBHaa CBOanMocxi, npo6nembi TO - >KnecTBa ana K, K npo6neme paapeuihmocth ana >, Hnane robopn, H n.r. ana K, HMeiox onny H ry»e cxenehb HepaapeuiHMocTH. STOT pe-, ykaabmaa na cymectbobahhe aosojibho TOHKOH aepapxha K.O. rpynn c HepaapeuiHMoft n.r., B TO xe apemh He aaet HHKaKoft HH<j)opMa - UHH nna KaKoii-jiHSo Knaccn4>HKaunH K.O. rpynn c paapeuihmoh n.t., -rax. KBK ace penypchehbie MHoxecTBa o6jianak>t oanoft ( HaHMeHfatueft ) CTene - Hfaro HepaspefflHMocTM. OnnaKO ana pekypchbhbix MHOKBCTB (H Boo6me ana paspeuihmbix anrophtmhhecknx npo6nem), B CBOK> onepeflb, raxxe Hbi paaniihhbie nepapxhh, xamaasi Ha KOTOPHX CBaaana c HeKoxopbiM HSHHeM nohstha cnomchocth npo6nembi (nanphmep, B xepmhhax cnrnanh3hpyiomhx 4>yHKUHH paanirhhoro pona (CM. B.A.TpaxT6H6poT C83), aepapxhh A.PjiceropHKKa C 10D nphmhthbho pexypchshbix MHOHCS CTB H T.a. ). flna rpynn c paapeuihmoft nposnemofi roscaectba Taxsce BoaHHKaer Bonpoc 06

2 M.K.BanHes HX KJiaccm )HKamin no CJIO>KHOCXH sxofi npo6nemw. B pa6oxe <I>.KaHHOHHx6 LI H npefljioacena Heicoxopaa aepapxna B xepmhhax fc -KJIBCCOB flna KOHOHHO nopojkflehhbix (xopone, K.n. ) rpynn co CHSXHWM HHC - JIOM onpenenaiomhx cooxhoinehhfi, HMeiomHx paapeuihmyio n.t. B aacxoaniefi pa6oxe npennaraexca cyraecxsehho 6onee xohkaa aepap- XHH nna K.O. rpynn no cnoscnocxh npo6nevifai xomnecxsa (B xepmhhax em- KOCTHBIX chrhajih3hpyioinnx MaiuHH Tb rophhra), Koxopaa B KBKOM-XO CMW - cne "MonenHpyex* B ananhxejifahoii cxenemi ahanoraihyio Hepapxuro ana pe- MHO»ceCXB. CymecxBosaHHe xakoft nepapxhh asnaexca HenocpeacTBGHHbiM cneacxxeopembi 1, xohhaa (JiopMynHpOBKa Koxopofi nphbefleha B 1. Coaep- >K3HHe sxofi xeopemh COCXOHT B XOM, ixo nocxpoenne rpynnbi K. no p.n. MHOxecxsy 5 Moscex 6wxfa ocymecxaneao xakhm o6pasom, HXO n.t. nna K a H npo6nema paapemhmocxn ana S csonaxca npyr K flpyry cpabhh - *) npocxo (c He6onbiiioft emkocthofi chrhanhshpyrameft). CymecxBeHHyw nacxb Bceft KOHcxpyKUHH cocxabnaex nphbeaehhoe 2,3 nocxpoeniie no p.n. MHoatecxsy > K.O. rpynnbi TV, o6naflararaell csoftcxaamh: 1) JV^ conep«<ht B Kanecxae noarpynnw cbo6onrpynny F c o6pa3yioinhmh CL, t> '< 2) nycxb fl & osoanahaex non - rpynny rpynnw F, nopo*nehhyio o6pa3yromhmh CL ucl, L&S \a -V<- conep»hx K.n. noarpynny Q^ xakyro, HXO Q f~l F = fl,... Hycxb AT - rpynna, HaoMopiJmafl rpynne W, cornacho H3OMOp4>H3My Z- : Ct ^-Q, Ct.N^. flna rpynnw /<, Koxopaa asnaetca CBo6oaHbiM npoh3benehh6m rpynn N u. W c o6i>eahhehhem cornacno X- noarpynn / 5» S Gtr H Q,. nerko nokaaaxb, HXO n.x. nna nefe n npo6nema Bxo%aeHHH B nonrpynny Q_ rpynnbi jvv aoao/ibho npocxo cboaaxca apyr K flpyry. C npyrofi cxopoabi, H3 npocxoro samenahha, Koxopoe cnenano 6 S~*~*~G: Vd. /?r,n us csoftcxba 2) rpynnw N^ OHesaaHbiM ospaaom BbixeKaex 3KBHBaneHXHOcxb: L. S " * CL GO. G Q r. T-e- npo6nema paapeiuhmocxh ana S npocxo csonnxca K npo6neme Bxo«neHHa B Q. riosxo- My fljifl nonynehha xeopembi, asanorhhhoii xeopeme 1 (xonbko c 6onee rpy- SbiMH onehkamh), nocxaxohho nokasaxb, HXO npo6nema BxoxaeHHfl B Q xax we aocxaxohho npocxo cboflhtca K npo6neme paspemnmocxh nna 5. B AHanorHiHbift peaynbxax nonyien B.A.TpaxxeH6poxoM B C12J, npm 3XOM OH Hcnonbsyex npyryro KOHcxpyKuaro rpynnw K,, HaabiaaeMyio HM KOHcxpyKUHeft HoBHKOBa-Byna.

3 O cnojknocth nposnembi Townecrsa n.ns rpynn HeKOTOpwfi cnoco6 nocxpoehha rpynnw.a/^, KOTOPHH MOJKHO HseneHb pa6otbi XHrMana C31I, paccmorpea KnanxsMOM B C6 D. HM nokaaano, HTO nposnema BxojKneHHfl B Q TH ana S 3<}>4>eKTHBHO CBOZIHTCH K npo6neme paapeuihmoc- OAHaKo, BBnny cboeft rpomosaicocth, KOHCTpyKuna ManonpnroAHa Ann nojiynehiia oiiehkh CJIOXHOCTH SToro cseaehha. nonyiehha Hy«Hbix OUBHOK B aactoaineft pafiore MW CTPOHM npyryio us OoaTOMy rpyimbi ^V. onnpaacfa Ha OAHy (necymectbehho HaMeneHHyio) H3 npeahaymeii pa6orbi tl 133. AoKaaarenfaCTBo TeopeMH 1 aaaepuiaetca TOFAB B 4 nocrpoehhem rpynnu K / *) XHUM cnoco6om, HSM Kf. neckonfako 6onee cno- KpOMe Toro, B 1 6yA6T nokaaano, HTO rontko Ha HajiHHHa oueaok, o KOTOpbix robophtca B reopems 1, oneht npocto BwreKaex TaSnaiHaa nposnemh paapeuihmocth AJia S n npo6nemh ToxtaocTsa ana K<- npyr K npyry. 3ro naer OTBBT aa Bonpoc, noctasnekhbitt HOM B C OcaoBHbie onpeaenehhs, ({KDpiviynHpoBKa H o6cy>kaehhe peaynfaratob, HeKOxopwe osrahe 1. AaflHM cnatajia HeoSxonHMwe onpenenehha. OnPEAEJIEHHE 1 C9H. EMKOcTHoft chrhannaiipyioineii MaiiiHHbi TbiopHHra 7~ 6yaeM HasHBart (JiyHKunio S_(W^ Koropaa pasna nacny aieen, HcnonbayeMbix MauiHHOft T npn nepepasotke c/ioea W. ecna MauiHHa H He onpenenena B HPOTHBHOM cnyiae. Iwl 4 n rae IWl o6o3haiaet A/iHHy cnosa \fj. Ana Sr (n.) coxpaahm HasBaHHe emkocthofi CHrHanHanpyioiHeH. B * Ao6aBneHO npn KOppeKType. FIocTpoeHHe rpynnw K ^ HCXOAHT H3 HeKoroporo nho<j>ahtobo-noka3atejifahoro npenctabjiehhh p.n. nonhhom c uenwmh KosiJxjiHUHeHTaMH. Ilpn STOM HHCJIO o6pa3yioinhx n HHCHO onpeflenaroinhx coothoiuehhfl rpynnu K ^ orpanhnehbi caepxy HeKOTOpwMH, aabhcanihmh or crenehji nonhhoma P H Hiicna nepemehhbix, B P,. JlerKO BHneTb, HTO nna Kaamoro p.n. MHOHcecTaa S npeacrabnehae MOHCHO Bbi6paTb rakhm o6pa BOM, HTO yiactbyiomhh B HGM nonhhom HMeer orpahhiehhbie csepxy He-

4 M.K.BajiHeB CHrHanHSHpyromHe HMBHHO xaxoro pona 6yayx ynoxpe6naxbca B KanecTBe jcpuxepha CJIOJKHOCXH anropiixmhhecknx npofijism. Hapaay c osbihhhm nohsthem MamnHH TbiopHHra B aanbheftiuem 6ynex ynoxpesnaxsca xak>ke nohaxae MaiiiHHbi TbiopHHra c opaicynom. HanoM- HHM 3TO nonaxhe, He BAasaacb B ero iioflposhoe (JiopManfaHoe onhcahhe(xo onpenenehae CM. ASBHC CHU ). Ilycxb /~ - npenmcax, onpenenehhun na MHcmecxse CJIOB B HexoxopoM anijmbhxe r. MauiHHa TfaropHHra 7" ( c -opakynoivt), KpoMe osbihhbix BHyrpeHHHx COCTOHHHS (r.e. coctoflhhfi, HaXOHHCb B KOTOpblX OHa MO»6T HHTBTb, HHCaTfa, CflBHraTbCH, H3M6HHXb COcxoaHHe), o6nanaex cneuhajibhbim cocxoahnem Q,y. (BonpocHxenbHoe cocxo flhhe). Oonaflaa B cocroshhe On i MauratHa nepexonnx aa OJIHH xakx B oa- HO H3 AByx BbiaeneHHbix COCXOHHHH Qo'^i B 3aBHCHMOCTM T TOFO, nemy pabho anaiehhe npenhkara I" Ha cnobe VV^,, asnaiomemch npoekuheft B 2^ anij)abhx 2j cnosa W, aanncahhoro na nenxe (B SXOM cnynae 6yneM robophtb, HTO cnenan aanpoc opaxyny o cnoae Wv ). u AnanorHKHO xoviy, KBK sxo caenaao Bbiiiie ana osbihhbix MauiHH TbiopHHra, MOJKHO onpeaenhxfa nohflrne emkocthofl chrhanhshpyromes xakjke H MauiHH c opaxynom. OriPEflE/IEHHE 2.EMKOGTHoii chrhann3npyk)ineji MaiiiHHbi c 6yneM Maabiaaxb (JiyHKmiio & (W), Koropaa pasna HHcny aneek, ncnonb -... ' r ayembix MamHHOft / nph nepepa6oxke CJIOBB W i ecnh MauiHHa ocxanabnhbaexca, H ne onpeaeneha B HPOXHBHOM cnynae. OnPEflEJIEHHE 3. ByaeM rosophxb, HXO npenhkax /"" csonhtca c cnrhanh3npyk)inefi V^Wj K npenhkary r, ecjin cymecxbyex MamHHa c opaxynom I, BbiiHcnaromaa npeahkax f~ H xakaa, HTO 33BHCHMO OX 5 CXenBHfa H HHCJ1O nepem8hhbix. A HM6HHO X3KO - BbiM 6ynex npeacxabnehhe 3^Cf,...,JCp PCZ.,^,^,...^^^} O, rae LL - p.n. MHOKecxBO nap naxypanfahbix HHCGJI, ynhbepcanbhoe ana acex p.n. MHOjKecxs,, - HOMep MHOJKecxsa S B cooxbexcxbyromefi HyMepa- UHH p.n. MHoacecxB. Oxcrofla aawirohaem, HTO cymecxayiox HaxypajifaHbie HHcna Cl H Z, xakhe, HTO ana nio6oro p.n. MHOJKecxsa S Moxex 6bixb acj)- 4>eKxnBHO nocxpoena rpynna /^, nna Koxopoft Btinonnaexca xeopema 1 H Koxopas HMeex He 6onee new q o6pa3yk>wnx H He 6onee IBM % onpeae - naromhx cooxhouieheft. ' rtphmshaa K rpynne K^ KOHCxpyKunro r.xhrmana, B. H X.HeftMaaOB (CM. Kypoui CIS I], cxp ), nonyiaem rpynny c AByMH o6paayroinh- MK H He Sonee HOM T. onpenenaromhmh cooxhomehhhmh, nna Koxopoil MO-»CHO nokaaaxb, HXO n.x. ana nee HMeex xy «e cxeneab HepaapeuiHMocxH, HXO H MHOJK6CXBO S

5 O CJKMKHOCTH nposjiemw ToxcflecTBa ana rpynn B aanbhefimem Hac 6yner HHTepecoBaTb sonpoc o CHOHCHOCTH cseae - HHH npyr K apyry anrophtmhieckhx npo6nem cnenyiomhx Tpex THROB: npo6- Jiewa paape UIHMOC TH ana p.n. MHowecTB uarypanbhux incen, saaahhbix B ynapaom an$abhte { 1 }, npo6nema ToacaecTaa flna K.O. rpynn H npo6nema Bx'oxaeHHfl B HSKOTOpyio nonrpynny K.O. rpynnu. Kaacnoft HS STHX npo6nem cootbbtctbyet npenhxax, ectectbehhmm o6paaom onpenenehhbiii aa TOM «e MHo«ecTBe, HTO H AaHHaa npo6nema; robopa o CBOflHMOcxH oflhoft npo6;iembi K apyroft, 6yneM HMert> B saay CBOAHMOCTb COOTB6TCTBylOmHX npeahkhtob. KpOMe Toro, H8M HHorzia nohano6htch 6onee cno xa.au npo6nema, HO npo6nema BxoxcaeHHa. HM6RHO, nycxb aaaa K.O. rpynna 6- H aekotopaa 66 nonrpynna H c o6pa3yiomhmh h..,/~l-,.... Torna TpeSyexcs no npo- HSBonbHOMy cnoby W H3 rpynnbi [j onpeaenrtb, nphhannejkht JIH W K H, H ecjiii npuhaane^kht, TO nonyhktb KaKoe-nH6o npeacrabnehae nna W B ospaayromnx /1^,/I2, TaKyro nposnewy B aanbhettuiem 6yneM HacHJibHoft npo6nemoft axoxneiuia B H. B nanbheflmem, Koraa STO cneunanbho He orosaphbaetca, non BxojKfleHHeM nekotopoft 6yxBbi, B cnobo 6yaeM nohhmatb TaK>Ke axo>kflehne 6yKBbi ±> 2. OcHOBHyro nacrb HacxoHmeft pasorbi cotasnaet cjienyromefl xeopembi. TEOPEMA 1. flna nio6oro p e K y p C H B H o nepeihcnhmoro MHowecTBaS cymectby - et K o a e i H o o n p e n e n e H H a a rpynna /C"^, ana KOTO.pofl BbinonHeHbi ycnobhfl': 1) npo6nema paspeuihmocth A n a S C B O f l H T C H K npo6neme ToacAecTsa A n H Kr c e w K O C T H o f t chraa/ihshpyiouiefi V(n.)=n. c aanpocom o p a s e H C T B e e a n H H u e o a HOTO c n o B a a. n u H u ri 2)npo6neMa ToacaecTBa flna K,. c B o - ahtcfl K n p o Q n e M e paapeuihmocth ana > c emkocthoft CHTH a n HaHpyioineft c aanpocamh o H H c n a x, He 6 o n b m H x IBM Wl. 3. Kax BHflHM, reopema 1 ouehhbaet ssahmhyio cno>khoctb S K npo- 6neMbi TOJKfleCTBa ana K ^ KpoMe roro, ecna S - pekypchbhoe MHO -

6 10 M.K.BanH6B >KecTBO, TO n.t. nna AC paapeuihma, H reopema nosbonaer nojiyniitfa Ana Hee "a6cojik>thbie* ouenkh CJIOHCHOCTH. B camom nene, MauiHHa c f -opasynom, BbiHHcnaioinaa npeflhkax r, B TOM cjiynae, Korna /" - 3<J>(J>eKTHBHbiH npeamsat, Moxcer 6wTb nerico nepectpoena B o6biihyio MauiHHy, TaiOKe BHHHcnaiomyio /"J (c acnonbao - o6bihhoft MaUlHHH TbIOpHHra 7", BHHHCJISIOmeft /" ). UplH 3TOM rex *HeanropHTMHHecKnx' T8KTOB, Korna MauiHHa o6pamaetca K opakyny, aoaaa MauiHHa BbmonHaeT pa6oty ManiHHbi 7" Haa aanpauihbae- MWM cnobom. HcnonbayH STO aameiahne, as TeopeMbi 1 nerno nonyiaexca TEOPEMA 2. Ana Kaxcaoro p e K y p c a a H o - ro MHOs<ecTBa [ cyraectbyer K.O. rpyn - na/<,ana KOTOpoS BbinonaeHbi ycnobha: 1) a n a niosofi MauiHHbi TbRapaHra J~, peiuawmeh n p o S n e M y To^necTBa a n si K, cymectsyet MauiHHa 7~. i na K O T O p o f t paapeuihmos H nna K O T O p o K Sr (n.) ^ S 2) ana nw6oh MauiHHbiT",na Koxopoft paapeuihmo5. c y m e c T B y e T MauiHHa 7~2, pemaromaa n p o 6 n e M y towaectba nna AC H nna K O T O p o f i 2 TeopeMa 2 nokaabiaaet, HTO tiepapxhs pekypchbhhx MHOJKBCTB cnojkhocth (B TepMHHax emkocthbix chrhanhanpyioinhx THna ST (n) ) nonnepehochtca na K.O. rpyrnibi, HaHHHaa c CHrHanHSHpyiomnx, pactyy no nopaflky KaK n., H Bbime, Tax icax npn STOM ycnoshh S n n.t. /( HM6IOT OflHHaKOBbie BepXHHe H HHXCHH6 OH6HKH CJIO5KHOCTH. B Aj, Ha TeopeMbi 2 H H3 cymectboaahha cootbetctbyromhx nphme - HO BwreKaioT cneayronuie ytbepacaehha (pent, seaae HneT o emkocthbix CHrHanHanpyioniHX rnna S_ (n) ). CHEACTBHE 1. FlycTtV- npohsbojibnaa no pob pekypchbhbix MHOKBCTB (CM. B.A.TpaxTeHSpOT C93 ) HenocpeacTBeH- pe- K y p c H B H a a 4 > y H K U H a T a K a a, HTO 1) cy-

7 _ OcnojKHOcTH npo6nembi TOscaecTBa ana rpynn 1 1 mectbyex M a u i H H a TfaiopHHra, ana KO - T o p o ft <^ aanaetca e M K o c T H O f t c H r H a - niiahpyiomeft, ry H 2) ^P(ri) 9- n. Torna cyme c T B y e T K.O. r p y n n a K ^, x a K a H, HTO 1) n K) 6 a a M a m H H a TbropHHra, peuiaiom a a H.T. a n a /<,-, H' M e e T e M K O c T H y r o c H - rhanhshpyioinyio, K o T o p a a no n o p a n. K y ne M e H b m e H e M <f(7~i); 2) cymectbyer M a m n H a, peuiaiomaa n.t. fljiak^c e M K O C T H O f t chrhajihanpy- KJ in e ft <P(rL). C^EflCTBHE 2. n y c T b ^ - npohasojifahaa p e K y p c H B H a a n s y M e c T H a a <{) y H K u H a. Torna cyinectbyet K.O. r p y n n a K ^, n n a K o T o p o H B b i n o n n e H O y c j i o a n e: ana JIK>- 6ofi MauiHHbi7~,peuiaioineft n.t. ana K ^, c y - 7-/ mectbyer M a ui n H a /, T a K M e pemarouiaa axy n p o 6 n. e M y, n p n H 6 M ana aocrarohho Sr Crr; ^ T: (ntsti CnencTBHe 1 nokaabibaex, HTO cyraectbyiot K.O. rpynnfai, ana KOTO - ptix nposnema ro*aectba HMeex ontxmanbhyio no nopaaxy chrhanh3hpyio - myio. CnencTBHe 2, Haofiopor, nokaabibaer, HTO cymectbyrot K.O. rpynnu c npo6nemoii TowaecTBa, emkocthaa chrnanhshpyiomaa ana Koropoft acer - aa aonyckaet cymectbehhoe ynynuiehhe. Bonee Toro, HS o6mhx cob6pa*e- HHfi (PM. LQH ) BbixeKaeT, HTO cneactbne 2 HMeeT Mecxo H npn nk>6om apyrom pasymhom Bti6ope HOHBTHH curhanhahpyioineft (ana cnrhanh3npyio - IHHX spemehh, pe>khma H acex apyrux, yaobnetbopaiomax axchomam BJIKD - Ma). 4. Ceftnac nokajksm, KBK HS reopemhi 1 MO»HO nonyhhtfa ytbepacae- HHe o Ta6nHHHoft cboflhmocth apyr K npyry npo6nembi paspeuihmocth S H npo6nemh ToacaecTBa ana K. j BO3MO>KHOcTb OHeBHnHbiM o6pa3om BbixeKaex H3 cjienyramefi nem- Mbi o6inero xapakrepa. J1EMMA 1.1. riyctfa npeahkar/t Haa M H o - 2 K 6 C T B O M cnob B a n f y a & H T e 2 c B o a n T - ana

8 12 M.K.BajineB c a K npenaicaxy/"' B a a M H O S C B C X B O M cnoa B aji<j>abhte2 c nomombio Ma - uihhbi c opaicynom, C H r H a n n a H p y i o m a s K O T O p O ft M3>KOpHpyeXCH 3<])4)eKXHBHOE $yhkhheftv.torna/^ C B O A H X C S K f~ T a - 6 n H H H o. IToKaxeM cnpabennhboctb JIOMMHI 1.1. Flo onpenenehhio xa6nhhhofi CBOAHMOCTH xpe6yetca yicaaatb anrophtm, Koxopufi HO nio6omy cnosy W B an$abhte S^ Aaex: a) KOHxponbHbifi Koprex <U.f, U2... <fw. >, roe U/,U.i,...,aK(wf cnoaa B amjmbhxe, H 6) 6yneay or K. (W) nepemehhux xaicyk), ITO anaiehhe /"^ ^\V) coanaaaet co HHBM -f (r<u,f), r (U.^,. >f~(ltkfw)))- BaSepeM B Kanecxse KOpxe»;a MHOxcecxso Bcex cnoa HJIHHH He 6onee H@M V(WJ B (4>HKCHpyH npoh3bojibhbift nopjmoic), a (JiyHKUHM -^ onpenenkm ospasom. Tlycrb «5/,&2,...,GX(W,>- HSKOTOpbift na6op Ha nyneft H HHU. Ana onpeflenehsra anasehha j- ( >f,<52,...,6^.. ) nocxynnm xak. Bw- AenHM Ha neare MaiiiHHbi ynacrok nnhhm V>(V/) H aanycxhm MauiuHy nan CJIOBOM W. Korna MaiiiHHa npaxoanx B cocxoakke O^, aanpaiiihbaa o cnoae LL-, cxabhm efe B coctoahhe Q&_, sacxaanafl pa6oxarb aanbiue; nph SXOM ace apemfl Ha6nionaeM sa TBM, Hxo6w, c OAHOH cxopohbi, rones- KB MainHHw He Bbixoflnna aa npeaenbi BMfleneHHoro ynacxka H,C npyroft CTOpOHu,. itosbi oha He aauhknhnacb aayxph axoro yiacxka (axo aenaex CH 9c j(})ekxhbho c nomorabro ciera HHcna XBKTOB). ECHH xakhm o6paaom K pesynbraxkbhoft ocxahobke MauiHHbi c OTBSTOM 0 HJIH 1, xo f (Of, C>2,...,GK(Wi) nonoxhm pashbim sxomy peaynbxaxy, B npoinx cnyiaax -f(6/,c>2,...,&k(wl ) MOMCHO onpeaenhxb npohsbonbhmm o6pasom. HenocpeacTseBHO HO noctpoeraui BHOHO, HXO ykaaahhbie Kopxesc H Synesa 4yaKnHH yaosnexbopaiox ycno»bsim RS onpenenehhh xa6nhhhofi CBOAHMOCTH. 3AME4AHHE. IlycTb sakhm-to ecxecxsehhtim cnoco6om onpeaene - HO nohflxne OIOJKHOCTH xafirihihott caoflkmocth oflhoro npeahxara K apyro - My (HanpHwep, nepes chrhajih3npyioinyio ManiHHbi TbiopHHra, no cnosy \ Koprex <.u./,c i,...,ti^.^)7'ta. 6yneay (JiyHKnaro j- ). AerKO HXO aoxaaaxejibcxbo nemmbi I.I. B aeftcxbhtenbhocxh ycxakabjih aaex 6onee chnbhoc yxaepxaehhe. A HMSHHO, ecnh aaaaua Mauinna 7"_ c opaxynom, csoflarnah ^ K /", xo no (JiyHitnHH V>, Maacopapyioineft HanHaHpyiontyio MauiHHbi T, MOXCRO ycxanosexb onehkh CTIOJKHOCXH xaxace

9 O CJIOXHOCTH npo6;iembi TomaecTBa ons rpynn 13 H nna Ta6nHiHo» CBOAHMOCTH r K T. HanpHMep, SCJIH V7 - HPHMHTHB- HO peicypchbhafl 4>yHKUHa, TO FI HPHMHTHBHO pesypchbho csoflhtcfl K r Til T.fl. 5. B aakjiroiehhe sxoro naparpa<j>a nphbeaew HeKOTOpwe HaaecTHHe reopethko-rpynnobbie peaynfaratbi, KOTOpfaie 6yayr HcnonsaoBaHbi B cneny KOTHX naparpa4>ax. Caanana BBeneM HeKoropbie o6o3hanehhfl. Fpynny c o6pa3yk>mnmh Of, Q,--- H onpenenaioinhmh coothomehhhmh &f =?2 =... = / o6o3haharfa nepes \QfQy, ' /2/ ^2=i--.= /i ECJIH H 6yaeM H /^ - nonr rpynnw rpynnw G i ro{h,f<} 6yaeT o6o3haiati> nonrpynny B &r nopoknehhyk) nonrpynnamh t-\ K. ECJIH & - rpynna c ospaayromhmh C^1,qz,... H Q/,Ki,... - cnoba B o6pasyioinhx fy,y2,-~', tf, tz, - TO nepes i7, 'ti,'t... ', G,~ R. =...:=/} 6yaeM ososhanatb rpynny, no - nynaemyra as C ao6abnehh6m o6pa3yiomhx &.,... H onpenenshoinhx co - OTHOUieHHfi /S =/=...= /. ECJIH nph 3TOM ao6abjiflembie COOTHOUieHHfl t> a-- 1; = ^- (a/;). U CY L/ Li w ~l U Lt] f,2,...)- cnoba rpynnti 6-, TO 6yneM robopntfa, HTO ~t- - npo- SyKBbi Haa rpynnofi Cr. Ecna f. saaaet HSOMOP^HSM noarpynnu /7., nopo>kflehhoft cnobamh <2/.-, j 1,2,..., Ha nekotopyro nonrpynny S3 G t TO / 6yneM HasbiBaTb npasanbhoft npoxonnoft SyKsoft Cl]. L B 2 HSMH 6yaex RcnonbsoBaHa cneayiomah nemma, Kacaiomaiicfl rpynn c npasunbrbimk npoxoahbimh 6yKBaMH. HEMMA 1.2. (BPHTTOH C43 ). 0 y c T b A/= { G, t,f,tz,... tiaijtl = ^Hy;' i>.j=t.2,~-} -rpynna c npa BH - j i b H M M H n p o x o f l H b i M H SyKBaMH^^,^-,... naa Cr.IlycTbW -cnobo B o6paayiomhx rpynnhi/-/ HtW paano e a H H H u e B/-/.To r- na nn6ow -cnoao B - o 6 p a s y i o m H x rpyn nw ^ «W P B B H O 1 B -,nh6ow coaepjkht O H H O H3 noflcnoa t~~;' at;,cl.a;, t; CLt~:. Ct Li Li L> t/ r a e # -cnoao H 3 ^ KpoMe nemmbi BpHTTona, HBM nohaao6htch cneayiomhe KOTOpbie KacaraTca CBo6oaHbix npohsbeaehhfi rpynn c o6i>eahhehho& noarpynnoft H nerko BbireKaiOT us reopembi o KaaoHHiecKoti 4>opMe ana. (CM. Kypoui C 15] ). TaKHX /IEMMA 1.3. (X.HeHMaa). Hycxfa^" -CBo6oflHoe ',

10 14 M.K.BanneB n p O H S B e n e H H e rpynn/? n E> c o6i>eflhheh- H o ft aonrpynno&l. n y c T b C H D ~ n o a - r p y n n H rpynn/? H B T a K H e, HT o Ci~i[_=DnL, M. T o r A a 1) noarpynna {C,Z7} e c T b c B o 6 o n Hoe n p o n 3 B e a e H n e rpynnc H JJ c o 6 i e - flhhehhoft nonrpynnoftn n 2){ C,D\ ft = C. AEMMA 1.4. II y c T fa F - cbo6oahoe npo - H S B e n e H H e r p y n n 7-^ H C^ c o 6 i e f l H H e H H- OM H 3 O M O p 4 > H b i x nonrpynn /?y H fl ( fl f nonrpynna HS ^, fl. - nonrpynna HS Cr ).Toraa Jiio6oe cnobow H 3 G p a a H O cnosy B nopmajifa- Hoft 4> o p M e Wx W2 W^, r a e HH a) w^ e Gf H«H w^ e ^2 ; B) w- n W-i, ne nejkbt oflhobpemehho HH L if " I B c) ecnn^?/, TO w<; 4 ^,. Vv^ ecnn y/ = /,TO cnoaa as r. >6Z-. (i 1,2...x)- cnosa us Cr, nw6oe as u.-, sa HH6M, 6bJTfa MOW6T, ZZ^ H i/, OTHHIHO OT eflhhhubl. Ha3OB M JIK>6oe H3 ti/ MHOHcHTenew caiosa W. Cnoso B nopmanbhofl <J>opMe, pabhoe W,, Mower 6biTb nonyneao cneaykdmhm o6pa3om: cpena MHOwHTeneft..,...,y paswckhbaem MHoacHTejib, nphhannejkamhfi o6ieanhehhofl nonrpynne, H, ecnn TaKOsoft Haflflerca (nna onpenenehhocth nycxfa OH npnrpynne Crt )> ero samehaem C/IOBOM rpynnu, pabhwm ewy, TBKHM o6paaom CJIOBO c MenbiuHM HHCJIOM MHoxiiTeneft n r.fl. ykaaahhufl cnoco6 nonynehna HopManbHoft (jiopmbi 6yneM B Hasbiaaxb cnoco6om coxpamehha HHcna Ha BwiiiecKaaaHHoro OHeBHflHbiM o6pasom JIEMMA 1.5. IlycTb^'- rpynna, HSOMOPC}) na a rpynne^r np«h3owopi})h3me:c' a ', f Cr ( cihtaew, HTO Cr ^ G == r ).Torna nphbeae- H H 6 K H O p M B J I b H O f t (J)OpMe C H O B P p y n - n u { r, G, CL= &,', CLG. fl\7 -HeKOxopaa nofl - rpynna rpynnu r,mo«;et 6bixfa npoae - a e H o 6ea ncnonb3obahbfl a o n o n H H -

11 O C/IOJKHOCXH nposnembi xcmaecxaa ana rpynn 15 x e n fa H bi x a H e e K na M a m H H e c o p a K y ji o M, peuiaramhm npo6nemy B x o j K a e H H H B noarpynny/7 ana c n o B r p y n n M G 8 2. OUGHKH CJIOWHOCXH HeKoxopwx anropnxmhheckhx npo6nem, CBaaaHHtix c rpynnofl M 1. KaK yxce ykashbanocb BO BBeaeHHH, ochobhyio nacxb KOHcrpyKUHH rpynnw Kr cocxaanaex nocxpoenne no p.n. MHOMcecxay ^ coaepkamefl cbo6oahyio rpynny c o6pa3yiomhmh Ci,u H ana KOTopoft cnpaaeanhbbi cneayiomre flba npeanoncehhh. K- - rpynnw//", H K.n. noarpynny Q^ npefl/lo^cehhe 1. tesxoraa H xonfako xora a, K o r a a oti'&clt' Q^. s npefljio)kehhe 2. H p o 6 n e M a B x o M c a e H H H B noarpynnystina c n o B rpynnw NC p e m a - exca Ha M a u i H H e cs ~ p a K y n o M c cur- HanH3HpyiomeH, He 6onfauieft, H B M Iwl, c sanpocamh o nncnax, He 6 o n b in H x H e M 2. nocxpoehhe rpyraibi N npoboflhxca, Hcxoaa us $HKcupoBaHHoro npencxabnehhh ana p.n. MHoxcecxBa : c x.,..., :C npo6eraiox MHOHCBCXBO nenwx nncen H TffL KOHIIOHK- UHa ajiemehxaphbix (JiopMyn onnoro HS BHHOB: ac C (L=0,1,...,m.,C=0,±1,±'2.>...), ^=X- (O^LJ^ m), Xm-1 xi+.xj=jck,xl-xj=xk (0< K< i<j <m), ozm=^ 2 BOSMOWHOCXB nonynehhfl xaxoro npeacrabnehha paccmaxphbanacb B OKOHiaxenfaHO nocxpoehhe W 6ynex aabepuieho B 3. A B SXOM naparpa<t>e paccmoxphm oahy KOHKpexnyio rpynny M, xoxopaa HecymecTBeHHofl MOflHtJiiiKauHeft rpynnw M, oscymcaaaiueftca B C 13]. Flpn SXOM see yxsepxcaehha, nokasahhwe B C13H ana rpynn bi M, c cooxaex - H3M6HeHHflMH nepenocaxca H Ha rpynny M CacU ososhanaex aenyio nacxb HHcna X..

12 16 3. OnHcaane rpynnbi M yno6no R&tb no 1) FlycTb = {a^.a^c,,^,^,^... aw^n.cm} CBoSonnaa rpynna. 2) ^ nonyiaerca nosabnehhem K C- o6pa3yiomhx t>o,'t1,...,t>rn-& on penenaiomhx coothomehhft: 6) 0,.,..., t^kommyrnpyiot co scemh octanfahbimh SyKBaMH rpynnbi. 3) M nojiynaercfl no6abnehnem K r ospasyromax Ct, < // <i a) dta.nd=l iri. i * \ 2 ttt ftt- * 6) cl KOMMyrHpyer co scemh octanbhbimh 6yKBaMH us & ; v^ c/ ^'K = ^^^ ; r) ~t--.j KOMMyTHpyer c ^ H co BCBMH ocxanfahbimh 6yKaaMH H3&. LI K K J 0 _L B nanfaheftiuem «iacto BMecro SyKB a.fflvo,t., 6yaeM nacarfa npocro &,&,. IloHTH SyKBanbHbiM BocnpouaBeneHiieM flokaaatenfactba npen - JIOWBHHH 1 us 3 pa6otbi C13H nokaabmaetca, HTO 6yKBM t/oj't,t,.,t't aajihk)tca npabhnbhbimh npoxonhhmh 6yKBaMH nan Cr, 6yKBH d &-.- / LJK npabhjibhhmh npoxoanbimh 6yKBaMH Haa (} ; H, HO, HMeex MecTO nemma (H==>K oahanaet, HTO H BKJiaAbiBae-rca B/^): HEMMA 2.1. G =3&I==1>M. 4. BseneM HeKOTOpwe osoahanehna (ananorhhhbie xew, Koxopwe aaeilshh B Cl3j. a) rtyctfa < 0^0,^C.,...,Xfrl> - uenohhcnehhbifl BSKTOP. O6osHaHHM H nepeaa.,^^...^- C.OBO ^...^^/oc^... ^>" 6) O6o3HaiHM nepea ft nonrpynny B 0, noposcnehhykf BCGMH B) IlycTfa X - MHOKecTBo BeKTOpOB. Torna fly 6yfl6T o6o3hanatb

13 O CJIOKHOCTH nposnemm Toa<aecTBa ana rpynn 17 noarpynny B /, nopojknehhylo TGMH CL, y flna KOTOpux ^Xi7,X/,...,X/T1 > X. ECJIH X - MHOW6CTBO HCTHHHOCTH (JWpMyJIH A*, T.e. BM6CTO MHO>KecTBo Bcex BeKTOpoB < X^,,X/,...,Xrrl >, ynobnetbopaiomhx A", TO _ r) AJIH anembhtaphbix tjiopmyji BMGCTO ft - BBeneM cneuhanbuue 060. HMOHHO, fljia (Jiopwyn BHfla: X^= C, X^=-X-, X^+ ^/~ *-K > X X-'X-=X.., X/TZ= 2 m~' r = 4- cjieaywiueft nemmbi KoimpyeT aoxasatenbctbo npenno- *) 2 H3 3 pa6otbi C133 /IEMMA 2.2. Una K a > K a o f t a n e M e H T a p u o f t (jjopmynbi/"" B rpynnea7 c y m e c T B y e T K.n. n o n r p y n n a L, r a K a H '^TO^^7 =.fl. H M e H - H o: 6) Lj' B) r) ^= 5. Ceftnac npncrynhm K paccmotpenhk) HeKOTOpwx anrpphtmhieckhx npo6nem, cbsaahhbix c rpynnofl M. CymecTBeHHbiM ana Bcex na.ifahefluihx paccmotpehhft 3Toro naparpat})a 6yaeT (j)akt cyiuectboaahha (CM. dime nem- My 2.3), ana icajkfloro anemghta rpynnbi M B BHfle eahhctsehhoro KanoHHHecKoro cnoaa, o6naaaroinero cnenyroinhmh 1) na6o oho(kahohhieckoe cnoao) HMeex ana Ta, rae T - cno - BO B ospaayrornhx t>o,t.,...,~t Q - cnoso HS &, T H 0 HecoKpaTH - MM; 2) nn6o OHO ecti, HecoicpaTHMoe cnoao Buna W; Z1 Vv' ^... Vv^, Z VV^.^_, W/,W2,...,W, - KaHOHHHecKHe cnoaa onacahhoro B 1) THna, nrosoe nemmbi MOJKHO npoaecth Taxwe, onnpascb Ha nokaobibaewykd HH>Ke nemmy 2.3. KN) B 3TOM nyhkte paccy>kaehhs cneayiox pa6ote C8H.

14 18 M.K.Ba/iHeB us t, 5 (S=1. Z...K) - oana HS 6yKB d vans., y (&= /), npnnem BW - nonnehbi ycnobha: a) ecnh Z, t,- (& =±/), TO nocnenhaa 6yKBa cnosa Wc OTi» C/^ ~*. I J s4 nhhha or,,, H OT npohasonbhoh 6yKBbi rpynnbi u ; At /t 6) ecnh _ = d, TO Ws ae oicahhhbaetca SyKBoii HS ^? ' ; B) ecna Z" = / f TO jm6o W, He OKaHiHBaerca 6yKBOft HS &, ^ HM66T BHfl Uc,1^,^ ( HJIH if^crn ), Tae 6^5 HG OKaHHHBaeTCS ^, (cootbetctb6hho 6yKBOH C ). /IEMMA 2.3. JlroSoft s n e M e H T naa/ npea - CT8BHM e n H H C T B e H H b I M K a H O H H H 6 C K H M cnobom onncahhoro swuie anna. flokasate/lbctbo. CymecxBOBaHHe Tanoro npenctabjiehhh HOHTH OHeBHflHHM o6paaom BHxeKaeT H3 onpeflenaromhx coothomehhh. flna Bbinon- HHMOCTH ycnobha 2,B) aamethm TonfaKO, HTO cnpaseanhbo coothoiuehhe: CL^ci CLmd 'ct.^ (ananorhhho nna C ^ ). nerko ycmatphbaetca nna npeactasnehhh Buna Ta. B camom nene, flba pabhbix cnoba W. H W- HS C- HMerar pabhbie npo- 6KUHH Ha o6pa3yk>nme to,tf,..., t^. OosTOMy ecnn Tia^=Tzaz.ro^=:7"2 Kf},==-<32, H B CHJiy HecoKpaTHMOCTH, Tf cobnanaet c T,a cobnaaaet c a CornacHO nemme BPHTTOHB, ecnn cnoso rpynnbi M, conepxcamee BxojKaeHHfl 6yKB d H ~t,., pabho enhhhue, TO OHO non>kho coaepacatfa I i noacnobo onhoro HS BHaos ( ^ - cnoso B o6paayioihhx rpynnw C- ) : *tf..k v tlflcho, HTO KaHOHHHecKoe cnobo He MOweT coaepwatfa TaKHx noncnob., npennonoschm, nanphmep, HTO W conep*ht noncnoao UK^^ ^aic KaK ^ necokpathmo, TO O HenycTO. C npyron CTOpoHbi, nepen SyKBoJS f/k He MO>KeT ctoatb HH 6yKBa t^ H HH H3 SyKB rpynnbi G, a tf HMeeT BHa Tq. RonynaeM, HTO Ct = / H 7 SyKBOii, OTHKHHOH OT "t^. TaK KBK 7" HecoKpaTHMO, no-, HTO ff ^ \C-t ik\ Paa6op octanbhbix cnyiaeb ahanorhnen. HenocpencTBeHHO Ha caenahhoro aamenahha cnenyet, HTO HHKaKoe cnobo y/ OT o6paayioiiihx rpynnw & He Mo>KeT 6biTb pasao KaHOHnnec - Kowy cnoby W, coaepacamemy axo^nehhe 6yKB d ann Z^/.v. TBK J & W, T3K»C6 K8K H W, H6 COfl6p>KHT BXOJKAeHHft noflcnob BHfla

15 O cnoxchocth nposjiembi TO>KflecTBa ana rpynn - 19 a), B), c). cnoba: Tenepb npeanono>khm, HTO B rpynne M pashbi asa W; Z, W2 Zz... W^ ^ W^, H w, T, W2 r2... W HM66M: ' w/'w, z, w,t2 TaK Kan 06 a cjioaa 6binH KaHOHHiecKHMH, TO B nonynehhom cnose noacno- BOM oahoro KB THHOB a), B), c) MOJKex 6biTb TOJIBKO cnoso W7 iv/f,. Orcrona cnenyer, HTO /t/='c/. Tenepb nokajksm, HTO W/=W/. Flpeanono - >KHM, HTO Z = cl (octanbhbie cjiynaa aaanorhhhbi). HMGBM: L,cL (L=o, t,...m-<), 4. (L=o,f,...,-m.i,a^n,czm\. z flyctb W, HM66T BHa Tf Ct /, V/7 HM66T BHA Tf O/.. TaK K3K W^W^ B (j, TO npoekuhh cnosa n Tf Tf Q/ na \.~t ~t /,...,'^ATT} pabha eaahhue. riosto- My r = 7". Ha ycnobha 3, B), nanokehhoro na BHa KaHOHHHecKoro cnosa, onebhahwm o6paaom BbiTeKaeT TaKace pasehctbo g = N. CnpaBeaJiHBocTfa nemmbi 2.3 nerno nonynaetca Toraa HnayKUHett nop. 6. PemeHHS Bcex Tex anrophtmhheckhx npo6nem ana rpynnbi M, o KOTOpwx 6yaeT nath penb HHKe, ochobahbi Ha nphbeaenmi CJIOB rpynnbi M K KaHOHHHecKOMy BHay. OanaKo npa nphseaehhh K KaHOHHHecKOMy BHay cno- BO MOJK6T CHnbHO yanhhhtbch ( HanpHMep, KaHOHHHeCKOe CJIOBO, pabhoe CJIO- / V /O 2C v By CL CL, HMeeT BHa Ct CL ); nostomy npnxoahtca nphmehhtb H6KOTOpbift cneuhanbhbih cnoco6 aannch cnos (B aanbhefiinem ana KpaTKOCTH raaanncfa 6yneM HaatmaTb KOBOM). Koa W cnosa W nonynaerca H3 W cneayiomhm o6paaom. IlycTb W HMeeT Bna^s 'j ^..3 / 2. K r,--.,$ ~ o6pa3yromhe rpynnw M -HTIH ospathbie K HHM / H at: >O (j = 1,2,..., K). O6o3HaiHM abohhhyrd aanncb> HHCJia oc 5es nepboft ea«hnubi sepes 5c (HanpHMep, 5 = Of ). Toraa ana nonynehha vv Hy«Ho B cnose W BMecTO Bcex noacnos BHaa ^ J (. - oana H3 6yKB O,^,G^,t ^, &=!, L OJ,..,!m, ) noacrabhtb cnosa J.< ".. BxojKaeHHe B cnoso W noacnoaa ^ot 6yaeM HaawBarfa ^ cnoea W. Ecna CJIOBO W coaepxht noacnoso BHaa CL d ' CL^, oc, TO ana yaosctba B aanbhefiiuhx paccyacaehhsx 6yaeM chhtaxb, HTO Bxoicae- HHH CL^, H ailot coctabnaiot oahy KOMnoneHTy (ahanornhho ana c ). m. m

16 20 M.K.BajmeB ycnobhh ; 6yKBbi > '. (i 7O) B CJIOBO 6yaeM HasbmaTb Ci -csosonhbim npa 1) ecjin i/, TO ykasahhoe exo>kaehne He B noncnobo <2-,-oc" u,-, 2) ecnh = /, TO yuaaahhoe BxowneHHe He -/ BKJlIOHaeTCH B noacjiobo &. d/oc. AnajiorHHHO onpenenaem nohhthe C - C u CBo6onHoro BXOJKA6HHH 6yKBbi ti (B 3TOM cnyhae Hy>KHO B ycjiobhh 1) roo noacjioae S/C-oi., B ycnobhii 2) - o noncjiobe C/oC u/ ). Bxo- 66 <^ C 6yKBbi t) 6yaeM HasbiBaTt, cnesa U. -CBo6oflHbiM, ecjth OHO He BXOAHT B noncnobo Cioo[-&o, H cnpasa CL - cbo6oahbim, ecna OHO He BXOZIHT B noncnobo aa CLn cc. HHCJIO a - cbo6onhwx Bxo>KaeHHfi 6yxBH > B CJIOBO W 6yaeM ososhanatfa sepea y^(c,cc), HHCJIO C -CBo6oflHbix BxcmaeHHft nepes W(L,C). W(0,O.) 6ynex ososhanatb o6mee HHCHO d -cbo6onhbix cjiesa H cnpasa Qyica vo. FoBopa o HHcne sxo>kaehhfl HCKOTOpOfi SyKBbI _ > B KOfl CJIOB3 W, 6yfleM HMBTb B BHfly HHC/IO BXO- )Kfl6HHH _^ B CJIOBO VV (B o6o3hah6hhhx: I W I j ). HM66T M6CTO CJI6AyK)maH /1EMMA 2.4. C y m e c T B y e r M a u i H H a Tbio p H H T a C 6 M K O C T H O H C H T H a J I H S H p y K ) 2_ mefi, He Sontuieft,. nem Wl. K o x o p a a Jiw- 6oe CJioBoVV r p y n n w M nepepa6atbiaaer B K O H K a H O H H n e c K o r o cnoaa, p a B H O r o W. /7 floka3ate.nbctbo. OycTb W HMeer BHH ^^...A^ (rne^j.^... ^~ ospaayiomhe rpynnbi M HJIH o6pathbie K HHM). O6o3HanHM nepea W- non- CJIOBO ^ ^.. ^. Pa6ora MauiHHbi pa36hbaetca aa n. MaKTpOTaKTOB. ff v B renehhe nepahix C MaxpoTpaKraTOB nponcxonht nojryiehhe xonaw^ KBHO- V" j v HHHecKoro cnoba, pabhoro cjiosyk^. OSosnaHHM CJIOBO V^e-/ > /> nepea W^. OflHoapeMeHHO c onncahh6m pa6otbi MauiHHbi KHnyKUMefi no C noka>k6m.. V nio6oro npomewytoiaoro Me>Kfly Wa u W^ cnoaa l/" cnpabeanhboctb cnenyromwx A) HHCJIO Bxo>KaeHHH B CJIOBO (S KOMnoneHT 6yKBbi CLO - He 6ojibuie,H6M ea e,,, 6oJibuie,HeM IW^I ^Iw,,! -W*~(C,a), KOMnoneHT 6yjcBbi C- - He L i, ^ 6onbme,HeM I W I. +- \Vf.\ W* ft C), KOMnoneHT 6yKBbi ±. - He c UL c u L 6ojifaiue,HeM I Wgl =6" B) HHCJIO BxowaeHHfl jiiosott HS 6yKB CL. C-(/<.rnJ& CJIOBO O - He P2(rn-i) L L, oojrbiiie,hem C, HHCHO Bxo«0eHHH 6yKBw t - He Sonbiiie. IBM

17 O CJIOHCHOCXH npo6nemt>i xojkaecxfia nnfl rpynn 21 He C) HUCJIO HH66X, SaHHTblX XOMHOHeHTaMH 6yKB (Zrn, BXOflHfflHX B tff "m f- u <- "rn iti - He Sojibiue, H6M Iv/^l^ (IW^.^.,, rv'^"y'rf ' "T^" Ha ytsepjknehha A) Buxexaex, HTO HHCJIO KOMnoneHT acex 6yKB, KOxopoe Morno noabhxbca Ha nenre, ne 6onee nem 31 WI ; H3 ytbep>kflehha B) BbiTexaeT, HTO nrosaa KOMnoneHxa 6yKB CL;, C;,~t; (i-^rn.), noas - L< ' c< t- naiomaaca B npouecce pasoth, iimeex.flnnny ne 6onee HSM 2m.LOQ 1WI ; Ha ytbepwaehha C) BbixeKaex, HTO HHcno aneex, aanatbix 6yKBbi CL i He 6onbiue,HeM lwlff +\y/\ -I wi^t-lwl^ -(I wl^-hwl^ ) <. (1Wlc ana C^ ). Kpowe xoro, HS onucahha anrophtma 6ynex SCHO, HTO B nponecce pa6orw HHCHO axo»cnehhft Syna ~U-cl,' ' ~b;:,, ne sospacxaer. OKOHHarejibHO nonyihm, HTO MaxcHManBHoe HHCJIO aneex, acnontayembix BO spemfl pasotbi, He Qonbuie. nem -~- + 6mtiff^ Iwl ~^~ 3l\Vl i T- e- ana noctatoiho 6onbiiiHx iwl CHrHannaHpyioinaa MauiHHbi MeHbme, IlepexoaHM K onncahhk) pasotbi MauiHHbi H K aokasaxejibctby yxsep - A), B), C). BasHc HHziyKHHH onebnaeh. PaccMOTpHM & -ft MaicpopaSoTbi MauiHHbi. I1epe6epeM ace BOSMOJKHOCTH ana &g. Bnonne ahanorhhen). cnynafl.= *-/( cnynaft t -1, AnropaTM pa6oxbi B STOM cnyiae saitniohaetca B 6yKBH t>; LI K Hanany cnosa W«tz~ i AO rex nop, noxa STO BO3MO»Ho; nph 3TOM Hcnonb3yroTca coothouiehha: ( 1) r7^-^='t^/7. ^ne n ;ih6o 6yKBa Or (j^l, L= f), nn6o KOMnoaeHTa oanott na GyxBCt- KUI &0 OQ &-Q, &~ 1 ) H OflHOBpeMeHHO npobohatca BOSMOKHbie H o6beahhehns cocenhhx KOMnoneHT onnofl H TOH >KG 6yKBbi. (CoKpameHHa H o6teahhehha xomnohenx, o Koxopbix robopiuiocb BHuie, HBJiaioxca cocxabhofi nacxbio anropnxmob BO scex paccmaxphbaewbix HHxce cjiynaax, H, BO HaSexcaHiie nobxopehhh, npn onncahnn STHX anropnx- MOB OHH ynomhhatbca He 6ynyT). Tlerxo BHflexb, HTO B onhcanhom npouecce xa>kaoe noaanehne Hosoit 6yxBbi CL- ymghbiiiaex HHcno Ci -cbo6oahwx 6yKB $ na c u

18 22 M.K.Bannes H, o6patho, noasnehhe HOBOfi Ct -cbo6oahofi SyKBbi u^ Mox.er Bbi3BaHO TonfaKO cokpauiehhem CL; -KOMnoHeHTbl, KOTOpaa CBaawBana COOT- Ls aetctbyromee sxo>kaehne SyxBH c7/ (ahanomiho ana C- ). Kpovie roro,, HTO HHCJIO KOMnoHeHT SyKBH ~t^ ybejihhhnocb ne 6onee Ha 1. Oxcrona Bbirexaer cnpabejjnhboctb ytbepscnehha A). CnpasennHBOCTfa yrbepjkaehha B) BbixeKaer HS xoro, HTO nph npobenehhh ykaaahhoro npo uecca HHCJIO BxoscneHHfi SyKBbi CL; (6yKBbi C,- ) ybenkhhnocfa He 6onee IBM O L/ HalW^I^. (ana G-o He Sonee HBM Ha 2 V\^- ^ ), r.e. o6mee HHCJIQ BXO» - 6yKBH CL- - He 6onbiue HSM (C f) rn ^ &. 4Hcno L- SyKBfai 6- Boo6me He ybenhhhbaerca. HaKOHeii, ytbep^kaehhe C) LI H3 Toro, HTO HHcno HieeK, aanatbix KOMnoHeHTaMH Kaxaoit HS 6yKB ^2/T7, C/rz, Boofime He ysejitihhbaetca, xorfla ^= Z^/ (.L^=-mJ,H BH cl ne 6onee HGM na I Wg I ^ xoraa, = Z^/rl. 2) - == Oi. AnropHTM pa6otw aaknroiaetca B npoabhjkehhh 6yK K nanany cnoba, npa STOM HcnonfasyroTca coorhouiehha: (1) nct=dl7, rae T7 - nh6o oana HS 6yKB Q- (, /, L= m f), nh6o KOMnoneHra cnpabennhbocth ytbepscflehhh A) H B) HHISM ne OT- OT coorsetctbyioinhx nokasatenbctb B cnyiae 1). ytbep»cnehae C) BbrrexaeT HS TOPO, HTO nph npoxokflehhh 6yKBM d njihha Kascnoft KOM- 6yKB CLrrL,Crn ybenaiheaetca Ha enhhhuy, a HHCJIO KOMnoneHT /T, no npeanono«6hhk> HHnyKUHH, He Sojiee IV/^I^ H- I W I,5 CHS 6onee HBM 'W^l^ +'^l/ ) 3) 5» = C^~*. B 3TOM cjiynae nponbhjkehhe 6yxBbi c K Hanany CJioaa ocymectbnaetca B COOTBeTCTBHH c cootho-inehhamh: (1)^<2^ Ct,nt rae /? - jih6o 6yKsa u- (t^= 'i, Uf'fn i), jin6o KOMnoneHra oflhofi H3 OHBBHflHO. oc +- / (JU - oana aa 6yKB ^ H^). floxasatenbctbo nro6oro us ytbep>mehhft A), B) H C) cobepmehho 4)^==Zy-Af Cfc==i/j. PaccMorpHM noapo6ho cnynafi: =+/. Pa- 6oTa npohcxonht cnenyioinhm ospaaom: 6yKBa ^/^ npoabhraetca K Hanany cnoba, ncnonfasya coothoinehha: (l)/?.. ~tf- 17, rae n - nh6o 6yxBa c (. (JK y< c t a 6yKB GL

19 O CJIOHCHOCTH npo6nembi ixmnectba ana rpynn 23, tk ; (2) 4- (anecfa HcnonfaaoBano TO, HTO ~t H C- KOMMyTHpyror); npn STOM BHOBB, J nohbjiaiomnech KOMnoneHTbi 6yKBW ~C^ no Mepe noasjiehhfl nponbnrak>tca K naqany cnosa scjien sa SyKBofi ~t, Hcnojibaya cootberctbyiomhm 06 - it / paaom MonH(J)HUHpoBaHHbie coothomehhs HS 1). ytbepacnehhe C) B cnynae rphbhanbho (nanomhhm, HTO <^,j^.m ). yrbepkflehhe A) B TOH n, KOTOpaa KacaercH CL -KOMnoneHT H C -KOMnoneHT, He 6onee HSM Ha ejihhhiiy. B 1) paccy»nehh6m, a HHCJTO ~OK -KOMnoHBHT FIoKaKeM cnpaseflnhboctb ytbep*aehha B). flna 6yKB, ornnnhbix or CLK,CK, L K, nokaaaxenfactbo oieahflno. KaK BHJIHO na coothoinehhft, HHcno BHOBb noabhbahxca Bxo^neHHJi 6yKBbi ~t He Sonfaiue HHCJia Bxowaev * HUH 6yKBw C: B cnoao W/>_.. KOTOpoe, B CBOK> onepeab, no npeanono - I K,f i}2^-/)< rs H#**-*;-//«>K6HHJO HHZiyKUHH, H6 OOHbllie H6M (C 1} $ (C- f) ( HanO- MHHM, HTO x < I ). Orcrona HHCJIO Bcex BxoscneHHft 6yKBw ~t^ B nio6oe Mexay W H We CJIOB He 6onbiue HS H3 BHOBb noabhbuihxca BxowaeHHJi SyKBbi ~t K, npoxoaa nepes 6y- &» > nopojknae-t no onnoft 6y-KBe ci., H C^ HHCJIO BHOBB noabhb - " K, uihxca npn 9TOM 6yKB CLK ne 6onbUie IBM ( 1) *. OTCIO - fla HHCJIO BC6X BXO)KfleHHH SyKBbI O. H6 Sojlbllie H6M (, l) 4- nna C K ). 5) _5e - npoasbonbhaa Syjcaa rpynnbi r. B STOM cnynae sea pa- 6oTa COCTOHT B nojiyiehhh Kona cjioaa y, VVg H cnpabenniiboctb ytbep>kzie - HHft A), B) H C) npobepaerch TpHBHanbHO. /lemma 2.4. aoxaaaha. 7. Ha JIGMMH 2.4 BbireKaex BaacHoe ana aanbheftiiiero npeflao^ehhe 3. C e M K o c T H o f t chrhanhan- 2_ pyromeftlvvl p a a p e u i H M u K a w a a H na cnenyroihhx npo6nem ana rpynn H A/ :l)npo- 6 n e M a ToacnecTBa, 2)npo6jieMa BxoMtae -

20 24 M.K.BajiHes C = J- x H H H B n o n r p y n n bi A., A.. IQ^ //< m), A.. L.. 6 ;/ -^ 6/^C ' 6/A / >< K< 6</'< 7-n_; *i.' flokasatejibctbo. yrbepscnehha 1) H 2) HenocpeacTBeHHO H3 nemm 2.3 H 2.4. fleftctbhxenfaho, TBK KaK KaHOHHiecKoe npea - cnoa ezmhctbehho, TO a) we^ Torna H TOJIWCO Torna, Korna v. KaHOHHiecKoe CJIOBO (cnenobarenbho, H Ron W KaHommecKoro enema) W HS conepjkht HH OAaofi HS 6yKB ~t, d H ^/ > H B) W= / xorna V V H TOJIHKO Torna, Korna W - nycroe cnoao. Ka*floe HS STHX ycnoanft npo- Bepaercfl FlepeftneM K nokaaarenfactby yxbep>knehha 3).CHaiajia aamerhm cnenyiomee: nycrfa n - necoicpathmoe cnoso B o6pa3yk)mnx rpynnw (j, CJIOBa -' He coflep ~ Bxo>KfleHHft SyKBbi <. Toraa we/? a TOM H TonfaKO B TOM cnyiae, Koraa BbinojineHO Kaacnoe HS a) n HMeeT BHfl u. ' (l, &),,, ana HeKOTOporo < XQ, x/f..., * ^ *0 '*/ x/-n ^ 6) ana Kascnoro i, me 2 K, cymectbyet ' nyctfa BbinonaeHw ycnobha a), 6) H B), Torna \\, Ha npenctabnehh a), 6) H B). JlerKO BHnerb, HTO npencrabjiehhe (1) HecoKparHMO B, Tax Kax cokpatkmogti o6pa3yioimix a i+(h-f) d+f) <t-h) oahanana 6w, HTO B Of cokpamawrca BXOff-'^-i V/'-l'X'TJ ^ g< n o '. UosTOMy, TaK KaK HecoxpaTHMoe npeactaanehhe B ofipasyroiuhx a ana anemshtob nonrpynnw /7 SHHHCT - < ^ix^,...,xrr7> B0HHO, nonynaem, HTOO6/7, rae /""" - HSKOTOpaa (fiopmyna, Toraa H TOJibxo Toraa, Koraa nio6oft HS sektopoa < x^, xy,..., Xm > c, ynact- B ycnobuax a), 6) KB), nphnannewht MHoacecTBy HCTHHHOCTH

21 O CJIOWHOCTH nposjiembi TQMtAecTsa ana rpynn _ 25. AjiropHTM npoeepkh nphhanne^nocth BeKTOpa K MHoacecTBy HCTHHHOCTH sjiemehtaphoh 4>opMyjibi onebhaeh H He Tpe6yer AonojiHHTejifa - Hbix HHeeK nph peajihsauhh Ha MauiHHe TfaiopHHra. Kpowe Toro, HTO npoeepka BbinojiHeHHfl Kawnoro HS ycnobhfi a), 6) H B) T&KXG SbiTfa BbmojiHena Ha MauiHHe TbiopHHra Sea nphbjieiehna nonojimrrejifahbix aneeic, TBK KaK Kaixaoe us CJIOB u d) dj ( ) HMeeT fljinhy, He \+-...+\O. \ I CL\ TaKHM o6pa3om, nonyiaem, HTO npnnaane>khoctfa cjiosa g, HS Q- K nio6oh us nonrpynn fl-,/-! i (t L LJ * pacno3hana na MauiHne TbiopHHra c CHrHannsHpyromeft \o \ OneBHflHO, HTO 3TO HM66T M6CTO H B TOM CJiyHae, KOPfla BM6CTO Q / ero Kon. paccmatphba6tch OKOHiaTenbHo cnpaaeanhboctb ytbepjknehhs 3) BbiTexaex HS JIGMMH 2.4 H cneayjouihx nerko npobepaemwx ytbepxflshhji, yctahabnubaromax BHA KanoHHiecKHx cnos ana snemenrob nio6oh HS noarpynn, o KOTOpux pent B yxbepjkaehhh 3) npeanowehha 3: HAST (1) ecnh we/y.. TO KaHOHHnecKoe CJIOBO VV. pabhoe W, y C et BHA TQ, rae 7~ - CJIOBO B o6pa3yiofflnx ti~ CZ-7^6j, Q -fl; ', 7 _ Zs if L (2) ecnh vv e L~-, TO \ HMeeT BHA J '<y, TAB 7" - CJIOBO B 06- paayiofflhx t; t: H t-(t=^l,i}, qefl~^: \ j,7, J./ CJ (3) ecjin w L,-, TO w HMGGT BHA To., rae 7" - CJIOBO J.. " * B o6pa3yroranx t^t^, t:tk H tz (1i=L,j,K'), O.G fl ' ^K ; ^j t ^ * J _^ (4) ecnh W6 LJ::K < TO W HMeeT BHA To, rue J~ - CJIOBO B * (5) ecnh we texp, TO W HMeeT BHA 7^, /^ T^fr TK, -L (L O,t,,.., T; 7^= /, 6CJIH i u npenno»;ehhe 3 9. BseaeM HeKOTopwe ososhanehhh: TJ,/< SyAeT o6o3hahatt CJIOBO - nonrpymiy n.&m, C,^ \y nnbi M in B -noarpynny. KpOMe TOPO, sesae B aajibneiliiiem BMecro 6yKB CLQ, VQ, - 6yaeM /7. CL,f},t-.. CyMMy ctenenefi Bxo^KAeHHH SyKBbi S B CJIOBO W 6yoeM na aecom ^ B W H ososhanatfa nepes cueayiomyio nemmy.

22 26 M.K.BanHeB /1EMMA 2.5. n y c T b W - c n o B O B o 5 p a 3 y 10 IUHX rpynnbi AY. T o r A a ecnn W& B>, TO AOKASATE/lbCTBO. FlycTb W osoahanaet KaHOHnnecKoe cnobo, '-^ /-v f~*~' pabhoe yv. Tax KaK W G, TO W - CJIOBO rpynnw G. ECJIH W TBTfa, HTO W HM66T BHfl (/ U &... U ti Ba B o6pa3yroinhx a, O, otnhhhbie OT B o6pa3yiofflhx CL/, l,cf,...,o-rri,6rtl,c,! ^t npnhaone>kht noarpynne E> \Q..,L O,'t-1, 2...\ it f, Ci,..., U. ^ - O,..., (J^ - CJIOBB (f.^-l, ecna : = = O, Torna H Tonbxo Torna, Korna nk>6oe us cnynae, - S, OHO coflep>kht xots 6w OQHO BXOKfleHHe SyKBw $. B npoaecce npnaenehha en OB a W K KaHOHKnecKOMy BHny HeKoropwe axowae - HHH SyKBbi u MoryT cokpathtbca, a HOBUX Bxo>KneHnfl arofi 6yKBw He He coaep>kht BXO*neHHft 6yKB CL,o, TO W B. OosTOMy MO>«eM CHH- -.- OTMBTHM B W Te Bxo>KfleHHa 6yKBH -Q, KOTOpwe coxpanaiotca B Bcero aroro npouecca H, cneaobaxenbho, BXOBHT TBKJKe H B W. O if f /j / ^K 3TO Dynyr Bxo%aeHHa v, u,..., O. Torna cnoso W a cnobo W HMeeT BHA: y "»^ J> I W/... 6 O6o3HaiHM nepea oc^ '***' Bee 6yKBbi noe cnobo \v- HMeex na6o v <X + OC/ = <X/ He it U C PaccMOTpHM HeKOTOpoe cnobo & ' B cnobe w- HCHO, HTO KBJKof OC~' L * O~ CL L ct,, HCXOAH us BbiiuecKaaaHaoro, OHO HM66T BHA Ha ycnobha u & E> nerno nonyiaem, HTO Bee (U--)a 6yKBH CL B cnou.- paaeh aynio, T.e. H,

23 O cnojkhocth nposnembi TOwnecTBa ana rpynn 27 ft-^+i c*,^ - - _ O' _..# _ (2) KpOMe Toro, OTCJOH& (U- ) "+" (U-7) + Ha (2) H (3) cnenyex, HTO nio6oe aa /., a cjieflobarenfaho, u y/ noarpynne o rj W, rae / f, HTO (4) OUBHHM chanana Kaacnoe HSOC- B OTAejitnocTH. PaccMOTpHM cnynaft: L/ < L < K. ripocneahm sa HSMeneHHeM seca 6yKBbi Q. MeKny BXO - o ' H a ^+/ B npouecce nonynehhh W HS W. HTO BbinonneHHe cokpamehhji H npeo6pa3obahhk cornacho coothomenham, KOTOpwe nn6o He conepwar 6yKBbi &» nn6o ykaawbaiot aa KOMMyTHpo - BaHHe HeKOTOpoft 6yKBbi c CL, ae MBHSHOT Beca 6yKBbi CL B nio6om noflcnose. HosTOMy ocraetca paccmotpetfa BbinonneHHe npeospaaobahhfi Buna: = 2 2 ' ^ = e ^, 4> 1 09 O, / O, O,.K 5 i. 3aM6THM, HTO ecjih npeo6pa3obahne ykaaahhoro THna KacaeTca BXO>K- 6yKBbi O, otjinnhoro OT exoacaehhft o u H V ^', TO Beca SyKBH CL B noacnobe, aaicniohehhom Me>Koy Bxo>KaeHHHMH -o CH D He nponcxonht. Ka%aaa SyKBa ~t/, npoxona nepea 6 6, nopoxccnpasa OT Hee SyKBy CL, H, npoxonn nepea u ^ ', nopohcnaet cnec, OT Hee 6yKBy CL. UosTOMy, noncihtbibaa oomafi Bee oykb ij, KO- Topue npoxonat nepea D 6H O ^', MOWOM ouenurb o6mhii npnpoct y. seca 6yKBbi CL Me>Kay 6yK&aMn f> ' a o c'"l"/. B npouecce nojiynehha W us W nepea 6yKBy ^ ^ npoxonat see 6yKBbi ~b, KOTopwe BxonaT B \ npasee, HBM -g L, nepea v c ' npoxoasrr 6yKBw ^, KOTopwe BxonaT B W npasee, IBM V c '. KpoMe xoro, HOBUX sxo»cfle- HHft 6yKBbi t B TeqeHHe scero npouecca He noabjiaetca. OTcroaa nemo

24 28 M.K.BamaeB, HTO y. = f Ke ospasom : «:,*= I oc_ -1- of. -*-...+ oc I. L u I L nna nio6oro L, HTO 6). (W/V + ( Bee 6yKBW CJL B W pasen nynio, T.e. (W^^^ (W; } a) 6) aokaatibaetch anajiorhhho, Hcnonbayn TO, HTO sec 6yKBbi "t B W paseh x- Ha (5) H ytbep»nehhii a), 6) nonyiaem, HTO (X^- - TaK KaK B \ HMeeTca XOTH 6bi OZIHO BXO>KfleHne SyKBw ~u, nonynaem, HTO */ f'w' "'-I f * - n,,. [IW -/ 1 OC 4s 2 > oc = rn_cloc, \&.;, L u,f,...,x] -4= HepaBeHCTBO (4) aokaaano, H BMecTe c STUM aaaepiiiaetcfl floxaaaemmbi riyctfa S ~ HeKOTOpoe MHOJKB CTBO HaTypanfaHwx HHCGJI. O6oaHa- HepeSigg noflrpynny {>^, Le. S,at, V1tC^....,CLm. &m,crn] nbi M. Ha nemmbi 2.5 BbiTescaeT sakhoe nna nocnenyromero OPEfl/lO>KEHHE 4. FIpo6neMa E x o x a e H H a cnobay/ H3 rpynnbiaf B noarpynny^ ^ peiuaetch Ha MauiHHe cs-opaxynom

25 "BuXxBdo- gf or«nnowou o qj.h3ohej.oa OHSKOW \<~)'3'1 ' Q\n x 'TI ixoohwaird (f C/^I^O)] oaogoiu BUD BDJOX 'BDJOX ox^uox H BEJOX (5 99' ' Q} OXH 'wabhxuoii BDcsoxQ (9) xo WHHHHUXO ' wehhsuabxodsdii ^a / * XHinoiXeBdgo a WHJNHXBdxooaH WHaXdD qxbdbugo XSMCOFM SH -77 j "' '3+ '/^'^=7 9 f ^nn^auoii HWHmcuXeBdgo Hwwmrogoao '?'<2 XHinoiXeBdgo a ownxedsooeh ahhsi/abxonedu oxe J.8JKOW etths a OHBOHUBB r -j r "77 OXh 'WSBh^UOU OSJ8U Q~ P +" ' -f- 'x" -f X> zs77^ 77 j BaXOH83Bd - OXOX8H ixoxn Xwoieoy <7;9M ox ' Q raaxxg ghhetrxoxa xhwdstroo 8H /" t o 77 oaouo OHWO rag BXOX Hirog JS^?' ' ^ 9\u-iWJtfoii 77 aoiro EH eodmcbx BUJOX 'Btruox oaiuox H Btraox?3M oxh 'OHOB 'oaox oaogom 'j - ^7 7 \u XHweimBHHdii -77 oaoifd /" Him OXH 'xaxuai/o g'g rmwau en BDJOX ' 0 3 M 'oh«=tif8xbaop8iw ox ' -77 eaoifo oaontro BITD rag BXOX / xeoa BUIT OXH '«W,BXHHO watr/cg sod 7 ^7~'(-71) Huog 'xeehe XNH * «JirexHHi;oiioD BHHeheifaHdu eeg BHeHUouna qxng XO>KOW Bxdeaodii BXS OXH 'OHtTHasHo ' '77 a Z7 raaxxg Boea rauxh BaxoneaBd enaoirojc -77 aoiro xeoa BUD BoxsBdsaodu BUBHBHD sshjcuo woxe g -2 ^t / ' Q^f HUOS ' / =^ -/2 JMSHHdu ' ^LJ0'iiJO.'lJ~'v''"''y''Q''7^ xhinoixebdgo a aoiro xwdoxossh ntrox - 2/7'"'*!/7'^7 Baoiro J Q. '73 xhincuxcedgo a 2'77""'777 ''r> aouo xiqdoxoxen wdox - Z77'' " ' *7l''n 8Da "2V7277"'^?/77'3Y7 DHa XSSWH A\x _ A qxadxowooed BOXSBXOO 'ohiuexbaodeifq g73m ox ' a '^7 axxg 8H H j EH BaOIfO BOX - /A HUOg ' 7M 'OH<?LfeXBaon8UO 'H ox ' y' p' J- a^^g BHHSDxoxa xnwdedoo M Hi/og ( xeshs /V\ A t wsh sauog an BoieXeHiroiiOH woxe ndii '^'g SWIMSLT OHOBiraoo) M oaonabd ' Baouo oaoxoahhhohbx /v\x a BoxaBaiqxBgBdedaii M BITBHBHQ -woe A -Bdgo jmhmcuxdsuo XHKBUjiqa BHHsDaao ooanodu ' -1 UOg GH X B U O K H o ' M jjemoixdh C UUjCdj BUD B3XO8D3KOX KWel/gOdll HXOOH5KOI/O

26 30 M.K.BajmeB K HeMy c BonpocaMH o nphhan.ne>khocth K S nna scex incen: Ilpn srom H3 ycnobhh U-& {~6 -.,64 -p BbiTeKaex, HTO nk>6oe o KoropOM saflaerca Bonpoc opakyny, He MOMST 6biTb> 6onfaiiie HOM -. 3AMEHAHME. Kax BHHHO us nokasaxejifactba npeanoxehha 4, ecnh cnobo vv us rpynnbi M ne conepjkht Bxo>KneHntt 6yKBH ft, TO nna Hero nposnema Bxo>KfleHH«B B pemaexca na o6bihhoii MauiHHe TfaiopHara c Iwl 3. noctpoehne rpynnu /Vc H 1 H 2 1. FIpHCTynHM K OKOHHarenbHOMy nocxpoehhro rpynnbi W,. Ho xoay nocrpoehha cpasy ace 6yflyx paccmarphbatfach HeKoropbie anrophtmhnec - KH6 BOnpOCbl. OSosHaHHM nepes M rpynny, H3OMOp4>Hyio rpynne M npn HSOMOP - : a *-a(l>t aem. ITycTb B npencrabjiehhe MHOxecrsa S BxoaflT anewehtaphbie (xapmyjibi, 2,..., IlocTpoHM HeKOTopyM rpynny A^ cnenyioinhm o6paaom: o6pasyem GBo6onHoe npon3benehhe W" rpynn M H A/ c o6-beahhehhem noa - rpynn G K G > nanee 6epeM CBoSoanoe npohsbeaemie J^f nojiyiehhoft ir( > ijlfe) * i O I (*) rpynnbi M H rpynnw M c osieanhehhem noarpynn L, H /_, H rax.. ir(p~')' *- oanee, Konnaa CBOoonHWM npoh3beaehhem rpynnw J\ rpynnw c os-beahhehhem nonrpynn /. w.lt, (Beaae o6i,enhhehne nonrpynn npohcxoflht B COOTB6TCTBHH C TpHBHanfaHbIM H3OMOp<J)H3MOM: CL «- B e H c T B o: flokasate/ibctbo. XTBep>KfleHHe a) OHSBHAHO, T.K. see 2. HMeer M6CTO cnenyiooiafl HEMMA 3.1. a) tf(p} - K.O. rpynn a; 6) B rpynnew BbinojiHeHO pa- WU*-

27 O cnojkhocth npo6nemh TOjKAecTBa ana rpynn 31 nonrpynnbi smjiawrca KOHSHHO nopo>kaehhbimh. yxbepjknehhe 6) BW- H3 HSBeCTHblX CBOftCTB CBo6oaHbIX npoh3bea6hh8 C osteflhhehhofi noarpynnoft. floka*em ytbepjkashhe B). Hcno/ibaya HasecTHbie cboftctba CBo6onnbix npohsbeaehhft c o6iennh6hhoft nonrpynnoft, KnayK.uw.eii no D HTO = fl _ n ft n.. n fl. i z. p ri rt ' p CnoBa d cbosoaho nopokaaior B M nonrpynny > Y XL=0,+i.±2,...,1=0,1...,n\ '" '' rn Orcrona onebhahbim o6pasom nonyiaeivi, HTO /7_ ft /?_ r~l...fifl- = /? ri rz i 7 YrBep>KfleHHe B) onao osoahaieirae (CM. C63). riycrfa /7. H /7 - noarpynnw HeKoropoB rpynnbi %/. Torna nepea /7. /? SyneM ososhanatfa MHOcnoB rpynnw f, pabhbix B ^ cnoeam BHaa U.V /1EMMA 3.2. a) IlpoSneMa T O «A e c T B a AJIB is(p> rpynnbi^v paapenihma na M a in H H e Tfaiop H H r* a c e M K O C T H O H cur^hajihaupy 10 TTT Q H 2 Iv/l 5 6) ch/ifahbie npo6nembi B x o a c A e H H a aapeiiihmbi c C H r H a n a s H - p y K) m e ft Iwl. n p H i e M A n n H a n o n y n e H H o r o cnoba He Sontme i e' M Iwl. flokasate/lbctbo npoaeasm no HHAyKUHH. 1) FIoKa^KeM cnpabea - nemmbi ana rpynnw TV. Corjiacno nemme 1.5 npubenehhe K HopManfaHoft (jjopme CJIOB rpynnw JV" MOXBT SwTfa ocymectbjieho 6ea pac - na MauiHHe T,, c opaicynom, pemaioinhm npo6nemy BxowfleHHa B noarpynny G Ana cnoa HS M. CornacHO npea;io>kehhio 3, STOT opaxyn 6biTfa sameheh o6whhoft MauiHHOft T c chrhanhshpyioinefi I Wl. CynepnoaHiiHfl MauiHH 7"_, H T aaet osbihhyro MauiHHy TfaiopHHra c cnrnanh - 2 r^j 3Hpyiomefi wl, Koxopaa nphboflht nro6oe CIIOBO W rpynnw W K Hop-,j ij)opme W Buna jf. Vv^ W.. W^., npanfem Iw I < IWI. CnpayTBepacneHHa a) BbixeKaer rorna HenocpeacTBeHHO HS nemmbi 1.4, Teas. KaK n.r. Ana M H M paapeuihmh c cnrhanhahpyionieft iw YTBepjKAeHHe 6) BbiresaeT as cnenyiojhhx aameiahnfl, onebhahbim o6pa - BOM nonyiaemwx HS nemmh 1.4: A) y/em (HJIH W6A7 ) xoraa H xonjbko roraa, Korna Z- == / n Wy -

28 32 M.K.BanHeB CJTOBO H3 M (cootbetctb6hho W7 - CnOBO H3 B) y/e M. M Toraa H TojibKo Toraa, Korna Z^2,W/eA7, vs^ea/, 2) IlycTfa nemma cnpabennuba AJIH.//". Hro6bi nokaaaxfa ee cnpaana TV, TBK we, Kan B cnynae 1), nocratohho noxaaatb, HTO nphbenehhe K HopManbHofi 4>opMe cnoba W H3.A/" MOJKBT 6biTb npo - B6A6HO c CHrHanHSHpyroraeft Iw! H HTO fljihha HOpManfaHoft ^OPMH W* He 6oni.uie H6M v/l. Tax KaK yrbepwaehha, ananorhhhbie A) H B), B nan - HOM cnynae xak>ke HMBIOT Mecro. OpHBeaeHne W K HopMajifaHOfi 4»pMe Mower 6wTb ocymectbjieho osbihhbim cnoco6om cokparaehhh HHcna MHOJKHreneft. Una nonynehhh TpeSyeMbix OUBHOK aamsthm ronfako nsa cnenyroinhx : (1) nphhaajiekhoctfa HeKOTOporo MHOKHTBJIH LL HsvV", (L),. K K nonrpynne U.- Master otitb nposepeha cneayiomhm oopaaom: cnanais (/' ) Jia ana Li pemaercfl canfahaa nposnema axojkflehhh B M- (cornacno HH - 2 nykuhohhomy npeanono»ehhio, STO HcnonbayeT He Sonee IBM IWl aneek, nphiem fljihha nonynehhoro cnosa V~ He 6onbme HBM Iwl^, nocne sxoro 2 yxe ana c/ pemaerca c chrhanhshpyromeft I V\a sxo>kflehha B / ( ),r.l v^ / ( >, V *J (i> V L, H (2) ecnh (j L,, TO (Tax KaK u - CJIOBO HS M ) co- /* Lt OTBeTCTByromee CHOBO H3 M Cc ', pabhoe /, nonynaetca npocto noa - CTaHOBKOft B U BM6CTO 6yKB Q C 6yKB Q,, T.6. flrthha CflOBa H6 7 ' ybenhhhbaetca. JleMMa 3.2 aoxaaana 3. riyctb J^C - rpynna, H3OMOp<J>Haa rpynne TV cornacno H30Mop<})H3My t ~Q. *~Ci, CL&ff. Torna rpynny N HOCTPOHM KBK f t *, ~ *» CBo6oflHoe nponsbenehhe rpynn N H _f\f c o6i>eahhehhem noarpynn M in M cornacho H3OMOp<{>H3My X>, T.e. TVg KT = \N /A/-r,N c? ;k.=h.,rie L r L. Ms nemmbi 1.3 H ytbepacashhh B) nemmbi 3.1 oqebhahbim o6pasom HEMMA 3.3. nonrpynnofijm, M\n H // a B - naetca rpynna JA7, M,/L=/t,/Z.G/*7 }. Una rpynnbi W& cnpabezuihba Taxme cneayh3inah 71EMMA 3.4. a) Hpo6neMa TO«aecTBa nna rpynn u Wg paspeuihma c C H r H a n H a a p y - 2. K> m e ft IWl. 6) C H n b H a a n p o 6 n e M a B x o j K a e H H a B t "^ i nonrpynnyj/v.mjpaspeuihma c chraanh-

29 O CJIOJKHOCTH npo6nembi TojKnecTaa ana rpynn 33 a n p y i o i n e i i Iv/l, n p H H e M A Ji H H a n o j i y n a e- M O T O cnoaa He 6 o n b in e H e M \ I. AOKASATE/IbCTBO. Cnanana aamethm, HTO H3 JICMM 1.5 TGKaeT, HTO nphseaehhe cnosa W 6biTb npobeneao c CHPHanHSHpyiomeft Wl, nphhew ly/*l -4 I Wl. CnpaaeAnimocTfa ytsep>kaehhs MH 1.4. H 3.2 BH- HS //5 K HopMaJibHofi 4>opMe W^MOHCQT a) BbixeicaeT orcroaa, KaK obbihho,. c nomomtro nem- AoKa>KeM yxbepjkflehhe 6). IlycTfa W HMeer BHfl W. W,... W^.. By- (P) chhtarfa, HTO Z-> / avew (Koraa -^=/, aeno cboflhrca K nemf '^ i Me 3.2 ). IIpeanojiojKHM, HTO we j M, M \ Toraa ana v/ cymectbyer npenctaanehhe W B HopMantnoft ^OP1^6 Bnna ij t?...(/, rae s > / i *~*j Ka>Kfloe tf; Jie>KHT nn6o B M, JinSo B M H He nphhaflneacht ff MMB- L> VIC \ -- TaK nan nro6oe us cnos W H W HMeer HopManfaHyw (^opmy, TO coxpa - inenae nacna MHO*HTenefi MOweT SbiTfa TonfaKO B cepeahhe., T.e. \^=C'a, rue ' nepea W2. Tax KaK^e M H W, ^ M, TO > A/ OTcrona nonynaem, HTO (7 'w, M, T.e. V/. = t/i^ H T.O. Ec- JIH t^-s, TO HGKOTOpoe cnobo, He nphhannejkamee M, OKaaanocfa 6bi pabhbim enhhhue, nero He MO«eT 6wTfa. CnenosaTenfaHO, 'L == S u r i V W& = '. OSpaTHO, ecnh BbinonneHbi ycnobha: \ 6 M. M W-.M. A7 npn H6THOM i, \\f- M. M npa nenethom i,. v ' (i, < t) H W^. nphhannejkht A/ npa nenethom 1 HJIH /W npn H6THOM 1., TO W& {A/, A/ }. TaKHM o6pa30m, HJIS TOTO HToSw peiiihtb Bxo«neHHa B A/,M, aoctatohho npobeparfa Bee yxasahhbie npo6ne\iy ycnobna. Ecnn HcnonfaaosaTfa ana nposepkh STHX ycnobhft MauiHHy TbropHHra, pe - uiaroihyio chnbhyro nposnemy BxoxneHHa B M, M, cymectbobamie KO- Topoft ytbepjknaetca B nemme 3.2, TO MW MOX.&M rapahthposatb, HTO ana Kaxcaoro i I /. I + I U,. I < I W.- 1. U U L/ Hs 3Toro HepaaeHCTBa nerko no/iynaiotch cjienyroihhe HepaaeHCTBa, KOTOv pue cobmectho c nemmoft 3.2 nak>t Tpe6yeMoe ytbep>knehhe: (i> = f,2.... ^) 2) \tfl\2l-f ^14 IWl. HepaaeHCTBo 1) nerxo nonynaetch no HHflyKmiM. flna nonynehhfl HepaBencTBa 2) aamexnm, HTO