Osnovy teorii Galua.

5. IRoAno~uquotnnul1 p.96)4
2o. Ilyc'ii B COCTOHIT 13 IJJIKJIOB nOHOa51LOB S > 3:
B-= (1, 2 3 4...s) (s + 1,...,2s
PaCCMOTpHm B1 A'lBA, rute A ==(I 2 3);
B1=(2 3 1 4..s) (s~+1,..,2s'.
a BBK~
BBJ = (1 s3).
Ho B1 H, C iIeROBaTeJlbH-O, BB1 '-BXO1UHT 13 f3 l03TOMY Qce~Cfpwa
Tpex'inenHlbif ituimn, co~naiiaeT C
30, B COCTOIIT 143 Tpex,1IeHHbNX LU14K.OB. HlyCTb Hanpl14mep B = (1 2 3)
(4 56).. Bo3bmeMt A (2 4). Toutra B,1= A_'lBA =(2 43) (I 5 6)...)
BB, 1 (1 3 6 2 4). DTOT CJqyLqai Hl14BO1LHTC5H K cuiyqato 20.
40. B COCTOi-T 1 a33yJLBYLIbIHIX 1IMM(JOB. HIYCTb HaI,.fpmmep B =- (1 2) (3 4).
Boab~mell A 12) 5). I, -'jo.'iwia couwpamb n1O'CTaHOBKY K = ABA -1 B 1 _
- A (B- 1AB) —'. Ho B '"AB = (21s), r~ie s gii~a, B KOTOpyto B nepeBOJW4T 5. PaccMoTpw'4! xia cniy4a%-:
a) s = 5 (,apyrmmm cJIoBami, cymeCTByeT ILwcpa, KOTOpyio B OCTaBJJqeT
Hd meCTe). Toraa K (I 5 2), T. e. Q3 co)ewi)1T Tpex4JieHmbif w4Kim.
b) s4 5. K = (2 s) (5) Hcnylyiafl B cJimyf 5 np14BOJ4lHTC%1 K npeaiu-,aymIemy.
TaFCHm o6pa3oM ioKamaHo, MLT() 130 Bcex c.Tyqaaqx ti - nt, OTyiqa ciie-.AyeTq,f'ro rpynna "2,11 fIpocTaH1.
8. T e op em~a 28. CtimmeTplliect~aq rpynna S. npnl tt t coARepwtir -, Kpome '0iJu~of-epervi14HOfl rpylrnbi, tiopmailbHbUX )IenlTeJneik
A ~o ic a.3 a T en 1 C T B 0. (rB CIIJ1y Teopemb 27 HmeeT p9i,t IHJ1meKcoB 2,
ni
2-H lofomy IIoweT H4MeTb eiue i1opmaJnbHbiIA aenlIiTeJqb TOdlbKO ROP11AKa 2.
EcaR nHpeJn~oJo)KHTb, 4ITO TaKOBOtl CyIlteCCByeT, If COCTOHT 143 eal14FHIJkb FH
11OXLCTaiHoBK1 B, K0T0opaI JL0Jl?(Ha HtmeTb B1JIL (1 2) (3 4)..., To nOACTaH4oBK B awma1Ca flepeBOAtHTbCqB B cam~oO ce6si, ecain ee rtoaBCeprHyTb npeo6pa3OBafHHIo flH fnomoumr mio6ofl HO~JCTaHOBKti rpynHbi, Ho BTO HeBO.3MO)KHO,
Tal( KaK, B339B A =(1 2 3), mbi ilojlyqixm: A 1BA (23) (I 4)..
9. T e op em~a 29 (B~epTpaiia). CHimmeTp1liqeCKaR rpyuiia
npm n t>1 5 Be 14meeT nloarpyH, HHJLeKc KOTOpb1X JICmaJ 6bll mieicy 2
ti n. Bcsiicai noarpyrna uiwiHaKC ft JLoJKHa npi4 n ~:6 coBnaaaTb
c ciimmerpuqecKofl FpynuH10t OT 11 - 1 ium4)p, OCfaBi5IIoHWx OAHY 143
U14p 1, 2,.. - ft tia meCTe.
LI.o Ka 3 a 'r C b CTB O. OrpaulwI"lqcl AlC o~a.3aTeJlbCTB3OM, 4T0 BCIIKaH1-0 Uarpyrrna IHILecI( fi H13OMOp(1)Ha c.I
10. LRorycTHM)i -ITO (Bil COJLep'MIT noIJpyHHy;')-A 14HaeKca k, r~je 2 < k <it.
Bce conpsimielffle c ~1~ HioanpynnbI iimeOT B CH14J1 Teopem 2-1 14 28 ejwHH'-IHyto rpyrilly B Ka'1eCTBa;I epeceqeHI45. H03To~ly M0OMO, HlplMeIifliS H43,rlO)KeHHbhlA B Teopeme 22, 20 meTOJa nH~o pefflbl, Hdi~iT H30MOP(3HYIO C e,
rpynriy HOACTaHOBOK k-i4 CTerneHH. HOPMIOK TaKoiA rpyHnbI He mO)IjzT
O~aHaKo npeCBb~lllTb I?, 14T0 f1POTH4BOpeqiT TOMy, tITo nlop5I,[OK (21 ecTb it!
H 'iTo k~n.