ajire6pa h jiorhka. 12. m-3 (1973^249-268 yflk 519.48 ...math.nsc.ru/~alglog/11-20/12/12n3-1.pdf ·...

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Ajire6pa H jiorHKa. 12. M-3 (1973^249-268 YflK 519.48 MMrmMKATHBHblE KflACCbl A/IFEEP A.H.ByflKHH, B.A.rOPByHOB BaeneHHe Knaccw anreSp aBJiaioTCfl o6o6meHHevi KBasnMHoroo6 - H BBeneHbi lIla^aaTOM D2l,L13H , L 14 J . B HacToamefi paSore naer- ca CTpyKTypaasi xapaKTepucrHKa HMnjiHKaTHBHfaix KnaccoB. noKaabiBaerca , HTO Knaccu ^-^w -rpynn, RK^ -rpynn H (JiHHHTHO-annpoKCHMHpyeMbix anre6p (rpynn) aaxiaiOTCH HMnnHKaTHBHbiMH. CrpoHTca npninep HMnnHKaTHB- Horo Knacca rpynn, aaaaHHoro OHHOH HMnjiHKauHeft or KoneHHoro 'tacjia ne - peMSHHbix, HO He HEnasomerocH KBa3HMHoroo6pa3neM. noncHHTbtsaeTca HHC- no HMnnnKaTHBHbix Knaccos rpynn, aanaHHbix HMnnHKannaMH nnHHbi -ft- , Yue 8g-^= 4i . flaso nocraTOHHoe ycnoBue, npH KOTOPOM pennHHHO nonnwe nonKnaccbi .noKa/ifaHo-KOHeHHoro KBa3HMHoroo6pa3Ha asnaioTca KBaaHMHoro - o6pasnaMH. B paSoie asynaioTca K^accu anre6p, J} -annpOKCHMHpyeMtix OTHocHTenfaHO paBescTBa ( Bxo>Kfle HHa) , a raiOKe Knaccbi rpynn, $% - annpOK- CHMHpyeMwx oTHOcHxensHo conpaweHHOcTH. floKaabiBaerca, HTO STH KJiaccw CHfexHo-noKanfaHbiMH, ec.iH ffi ecrfa oSteflHHenne BosfracxaioiHefi yHHBepcanbHbix KJiaccos. B HeKoropbix nacrnbix cny - laax nocneniies yTBep*cneHHe Sbino aoKasaHo pauee HeftManoM CllI] . Bee K,iaccbi a«re6p npeanonaraiOTca a6cTpaKTHbiMH, cHrnarypa - npo- H3BO/ibHOft 4)HKcnpOBaHHoft, He conep^KaiueH npeanKaTHbix CHMBO.IOB. Aeropbi rjiySoxo 6naroaapabi fl.A\CMHpHOBy, non pyKOsoacTBOM KOTO- poro BbinonneHa nacToamaa paSoxa.

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Page 1: Ajire6pa H jiorHKa. 12. M-3 (1973^249-268 YflK 519.48 ...math.nsc.ru/~alglog/11-20/12/12N3-1.pdf · Ajire6pa H jiorHKa. 12. M-3 (1973^249-268 YflK 519.48 MMrmMKATHBHblE KflACCbl A/IFEEP

Ajire6pa H jiorHKa. 12. M - 3 (1973^249-268

YflK 519.48

MMrmMKATHBHblE KflACCbl A/IFEEP

A.H.ByflKHH, B.A.rOPByHOB

B a e n e H H e

Knaccw anreSp aBJiaioTCfl o6o6meHHevi KBasnMHoroo6 -

H BBeneHbi lIla^aaTOM D2l,L13H , L 14 J . B HacToamefi paSore naer-

ca CTpyKTypaasi xapaKTepucrHKa HMnjiHKaTHBHfaix KnaccoB. noKaabiBaerca ,

HTO Knaccu ^-^w -rpynn, RK^ -rpynn H (JiHHHTHO-annpoKCHMHpyeMbix

anre6p ( rpynn) aaxiaiOTCH HMnnHKaTHBHbiMH. CrpoHTca npninep HMnnHKaTHB-

Horo Knacca rpynn, aaaaHHoro OHHOH HMnjiHKauHeft or KoneHHoro 'tacjia ne -

peMSHHbix, HO He HEnasomerocH KBa3HMHoroo6pa3neM. noncHHTbtsaeTca HHC-

no HMnnnKaTHBHbix Knaccos rpynn, aanaHHbix HMnnHKannaMH nnHHbi -ft- , Yue

8g-^= 4i . flaso nocraTOHHoe ycnoBue, npH KOTOPOM pennHHHO nonnwe

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o6pasnaMH. B paSoie asynaioTca K^accu anre6p, J} -annpOKCHMHpyeMtix

OTHocHTenfaHO paBescTBa ( Bxo>Kfle HHa) , a raiOKe Knaccbi rpynn, $% - annpOK-

CHMHpyeMwx oTHOcHxensHo conpaweHHOcTH. floKaabiBaerca, HTO STH KJiaccw

CHfexHo-noKanfaHbiMH, ec.iH ffi ecrfa oSteflHHenne BosfracxaioiHefi

yHHBepcanbHbix KJiaccos. B HeKoropbix nacrnbix cny -

laax nocneniies yTBep*cneHHe Sbino aoKasaHo pauee HeftManoM CllI] .

Bee K,iaccbi a«re6p npeanonaraiOTca a6cTpaKTHbiMH, cHrnarypa - npo-

H3BO/ibHOft 4)HKcnpOBaHHoft, He conep^KaiueH npeanKaTHbix CHMBO.IOB.

Aeropbi rjiySoxo 6naroaapabi fl.A\CMHpHOBy, non pyKOsoacTBOM KOTO-

poro BbinonneHa nacToamaa paSoxa.

Page 2: Ajire6pa H jiorHKa. 12. M-3 (1973^249-268 YflK 519.48 ...math.nsc.ru/~alglog/11-20/12/12N3-1.pdf · Ajire6pa H jiorHKa. 12. M-3 (1973^249-268 YflK 519.48 MMrmMKATHBHblE KflACCbl A/IFEEP

250 A.M.ByflKHH, B.A.TopSyHOB

§ 1. CxpyxrypHaa xapaKxepncxHKa

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B anre6py X . nPH KOTOPOM B A HCTHHHW see 4>opMynbi H3 ^/ ,

— ti xaKwe HCTHHHa B A . AnHHoft HMnnHKauHH (1) HaaoaeM

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B Koxopofl HcxHHHa (p . Knacc ffl anre6p HaaoBeM HMnnHKaxHBHbiM, ecnH

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H TonbKO xex anreSp, B Koxopwx HCXHHHW ace HMnnHKauHH H8 7" . ECJIH

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(nn6o KonsHHaH) , xo Knacc vu 6yaeM nasbiBaxb ^ -i

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ecnH o at = 'K ; MynbTHnnHKaxHBHO aaMKHyxfaiM, 01 ,in It 71 — ov; pennunuo

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Page 3: Ajire6pa H jiorHKa. 12. M-3 (1973^249-268 YflK 519.48 ...math.nsc.ru/~alglog/11-20/12/12N3-1.pdf · Ajire6pa H jiorHKa. 12. M-3 (1973^249-268 YflK 519.48 MMrmMKATHBHblE KflACCbl A/IFEEP

KJiaccu anre6p 251

smnaeTca pemiHHHo nonnbiM. ({JHJibTp o- / nan MHQjKecxBOM

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r^ ^2 = n./IEMMA 1 . F l y c T b ^ Z - p e n j i H i H o n o J i H b i

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Page 4: Ajire6pa H jiorHKa. 12. M-3 (1973^249-268 YflK 519.48 ...math.nsc.ru/~alglog/11-20/12/12N3-1.pdf · Ajire6pa H jiorHKa. 12. M-3 (1973^249-268 YflK 519.48 MMrmMKATHBHblE KflACCbl A/IFEEP

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3 ) c o u e p > K H T e n H H H H H y r o a a r e 6 p y .

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no nopo>KaaK>mnx KOTOPBIX He npeaocxonHT 16 . HpennojiowHM, MTO A /. 71

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Page 5: Ajire6pa H jiorHKa. 12. M-3 (1973^249-268 YflK 519.48 ...math.nsc.ru/~alglog/11-20/12/12N3-1.pdf · Ajire6pa H jiorHKa. 12. M-3 (1973^249-268 YflK 519.48 MMrmMKATHBHblE KflACCbl A/IFEEP

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TEOPEMA 2. 0 y c x fa # > max ( $ 0 , U"3 I ) • T o r n a

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H M e e x M 6 C T O p a a e H C T B O

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BHIO, nna jiioSoro X: £ /^ ^TlB^J)^ (A,fe /^) , rue

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.,

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1) n o K a j i b H b i f t ;

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flOKA3ATE/lbCTBC. ECJIH Knacc tfl onpeae^aerca

(2)

Page 6: Ajire6pa H jiorHKa. 12. M-3 (1973^249-268 YflK 519.48 ...math.nsc.ru/~alglog/11-20/12/12N3-1.pdf · Ajire6pa H jiorHKa. 12. M-3 (1973^249-268 YflK 519.48 MMrmMKATHBHblE KflACCbl A/IFEEP

254 A.H.ByaKHH, B.A.rop6yHOB

TO, OH6BnaHo, CBO^CTBO 1) - 4)

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Page 7: Ajire6pa H jiorHKa. 12. M-3 (1973^249-268 YflK 519.48 ...math.nsc.ru/~alglog/11-20/12/12N3-1.pdf · Ajire6pa H jiorHKa. 12. M-3 (1973^249-268 YflK 519.48 MMrmMKATHBHblE KflACCbl A/IFEEP

Knaccbi anrefip 255

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Page 8: Ajire6pa H jiorHKa. 12. M-3 (1973^249-268 YflK 519.48 ...math.nsc.ru/~alglog/11-20/12/12N3-1.pdf · Ajire6pa H jiorHKa. 12. M-3 (1973^249-268 YflK 519.48 MMrmMKATHBHblE KflACCbl A/IFEEP

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1. A.H.A/lA/lbLIEB, AnreSpannecKHe cncT6Mbi, HayKa , 1970.

2. A.H.MA/IbUEB, HecKonbKo aaMenaHHfl o KBasHMHOrooSpasHHx &n-re6paHiecKHx cacTeM, Anre6pa H norHica, 5 , Ns 3 (1966), 3-9.

3. A.H.MAHbLIEB, O HeKOTOpwx norpaHHHHbix Bonpocax anreCpbi HnorHKH, 'Tpynbi M6>KnyHapoaHoro KOHrpecca MaTeMaTHKOB, MocKBa, 1966*,MHp , 1968, 217-231.

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268 A.H.EynKHH, B.A.rop6yHOB

4. A.H.MA/lbUEB, O6o5meHHo HMbnoTeHTHwe anre6pbi H HX npiico -eaHHeHHbie rpynnw, Mar. c6., 25, N? 3 (1949), 347-366.

5. M.M.KAPrAriO;iOB, K).M.MEP3/lflKOB, OCHOBW xeopM rpynn,HayKa , 1972.

6. M.H.KAPrAnO/IOB, KXH.MEP3;iflKOB. BecKOHenHbie rpynnw, Bc6. "HxorH HayKH. Ajire6pa. Tonojiorna. reoMerpHH. 1966", MocKsa, 1S68,57-79.

7. B.H.PEMEC/1EHHHKOB, tjjjjHHTHaa annpoKCHMHpyeMOCTfa rpynn OT-conpajKeHHocTH, Cn5npcK. Mar.x.., 12, Ns 5 (1971), 1085-1099.

8. M.C.1IA/1EHKO, HecKonbKO aaMenaHHS o 6ecKOHeiHbix npocrfaixrpynnax, CH6HpCK. Mar.JK., 4 (1963), 227-231.

9. H.fl.AflO, O HiuifanoTeHTHbix anre6pax H p -rpynnax, HAH CCCP,15, N? 8 (1943), 339-342.

10. T.FRAYNE, A. C. MOREL, D.S.SCOTT, Reduced direct pro ducts, Fund.Math., 51, K3 (1962), 195-228.

11. B.H.HBUMANN, Properties of countable character, "Congres In-ternational dee Mathematiciens,I970", I (1971), 293-296.

12. A. SHAPAAT, On implicationally defined classes of algebras,J.London Math. Soc. , 44, 173 (1969), 137-1*0.

13. A. SHAPAAT, On the structure of certain idempotent semigroups,Trans. Amer. Math. Soc., 149 (1970), 371-378.

14. A. SHAPAAT, Subcartesian products of finitely many finite al-gebras, Proc. Amer. Math. Soc. , 26, N3 (1970), 401-404.

x5. R.BAER, Abzahlbar erkennbare gruppentheoretisohe Eigensohaf-ten, Math. Z. , 79 (1962), 344-366.

nocTynnno 20 anpejifl 1973 r.