Osnovy teorii Galua.

~ 3. Hopmeatibnbie JeximeAa 2

29

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B iueHTpe Bffl4maH14, TO maCTO HaublBaIOT Ta1~we 31IemeHT B- AB Co 1]p sIKCeRH bl M C 3JlemeHTOm A.
B HOBeit~ellenH.lTepaType- cof7p1mKeHHble 3JaemeHTbl qaCTO o6o3Ha,-aloT Tai{:
1 13
W-AB -A
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2. Te op ema 15. HOpRIj~Kl CO11pfDReH~bIX aae1vieHTOB paBibl.
o~K a 3 a TeA b CTB O. EcAiii A B-'AB, TOA~2 B-'ABB-'AB~
Bl'A2B;.tamee, /1 -A$2. A ==B-A2B.B1lAB -= B- A3B,_H T. A. Eclm
A M j, To Am' BWAmB = B1JB — J. H03TOMy 11opaJoK A He mome{T
6bn'b BbIwe1 nop~uita A. O6paTHo. ecalH A -tB_'AB, TrO OTCioaia A
= B4B1, 'H TaKHim o6pa3oM ecJiH A" = J, TO H A' B 'B-'==B]B-'=J.
C~eiaOBaTe~nbHO IIOPfI.KH 06014x 3JemeHTOB paB~bl.
3. Hpeo6paaoBaHHe UOJWCTaHoBoK. Ectiw meIMeHTbI rpynriu 5IBJARIOTC5I
nOJLCTaHOBKamH, H npHiTOM nO~jCTaH1OBKa A 3aflHCaHa1 B tU4KJax, TO He TpyIAHO,
He HlPOH3BOJLH )jegCTBkif1, HanHICdTb nlpeo6pa3OBaHHylo IOJaCTaHOBKY. a1IJIS 9Toro
TOJIbKO HY)KHO HpOH3BeCT14 I1OXCTafHOBKy B Haxa Lumcpamii
iBbipa)1aoIui~Hm1 A B wimHJax. B camom LaeJe, HYCTb
Torjia
B- IAB=
A nepeBoiuuuT B k, B FIepeBOAUIT k B a., TaK14M Otpa3OM B_'AB tiepeBOJW1T Mi B 0C, k14 mbi timeem:
B-'AB - ~ x~,... t)..(awl.. cj
39To emie pa3 11OJ1TBepx4(ae~F TOT Op aKT, 'ITO nOP5A1O1( H'3,1CTaHOBK1H He
meH~1eTC51 OT npeo6pa3oBaiiuH: JaeflCTBRTeJ~bHO, cor~iaCHiO ~ 1.11 IIOP5IJILOK noxarTaHOBK14 eCTb HaMMe~buIlee KpaTHoe OT HO~pSIIIKOB ee tUIKJOB, B TO BWMfI
im~ OT Hpeo6pJ,300aHHH 1L1~KJlbI OCTalOTC14 Heli3membiHbIM1
Y ii p a ~K B et H iie 13. fHyCTb. A (I 2 3), B = (I 2). H1poBepluTb iieHocpe~tCTBeHiblbM BbI4HcaeH~em, tITO B-'AB =(2 1 3) =(1 3 2).
YB pa)*cH e iiqe 14.,l~)%a3aTb, 'ITO 3JnemeHT, o6paTHbri1 K HpOH43BejHlenIO, pa~eHi
fplPO3Be~LeHu4o a~ieCeHTOB, o6paTmblx K 9jieMeHTaM-MHOWHTeqWm H B3RThJX B o6paTKIOM rOPIAp~Ke:
(AB)-' — B-'A-, (ABCf"i = C1B1'A-1, 14 T. 4.l
4. Hlpeo6panoBaHHe coBoiKynHoc'rei H rpynrt. noJL n p e 0 6 p a 3 0 B aH e m CO0Bo0K Y n 0C T It 3JiimeHTOB rpynn~bi MN 6yaem HOB14MmT OJHO