Osnovy teorii Galua.

24

24 ~~~~~~~I. rpynrzi

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Bce HoJaCTaHOBL(H COripsw>eHHOfl CHCTemb1 % B CHJIM Teopembi 8 He'-lTHbl.
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TaK KaK nO~JCTa11OBKa SVT- B CHf1Y Teopembi 8 qleTHafi H nOTOMY BXOJLHT R
rpynnly W. TaKHM o6pa3of AM! IlO~lyqaem:
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3HBKonepemeHHOtt rpyHlnbl n-of! CTeHeHH pa~eH
OTmeTHM CJeAtyfonLI Ba}KwiFI daKT:
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MO)KHO npeaCTaBMrb, K ai( npO1-3BeaLeHHe Tpex'-jjeHHbIX LLHKJIOB.
0o K a 3a T eJb C T B o TaK 1(aK K3aKJ1po I1OACTaHOBKY 3H3KoIepeMeHHOA
rpynflhb MOWKHO TipeRnCTaBIITb, KaK flPOH13BejieHHCe qeTHoro E4Hcjia TpaHCI1o3HL1H1,t TO aOCTaTO'IHO JaoKa3qTb, 'ITO npMBeem X ByX TpaHCnO3HUHR MO>KHO
npeACTaBHTb, 1(aK FIPOH3BeJ~eHlHe Tpex'IJIeHF~b1X [JHKJIOB. 3Jlecb mo>KeT BCTpe'FHTbCII OILHH 113 JtByX cJlyq-aeB: HJ1IH o6e TpaHcHO3M141HH cOuepwK3 o6niyio
U1u4)py, 14111W BCq BXOJI1flLHie B Hix LLH(~)pbi pa3.YIHHHbI.
B nepBOM cniy'ae: (1 2) (2 3):zz(I 3 2).
BO BTOPOM cJlyqae: (1 2) (3 4) (1 4 3) (1 4 2).
10. H1 p H M e p. CHiMMCTpH'IecK3a rpyirna 04 4-h CTeflCHHi COCT0OUT 113 cne~1yiouu1AX
4! 24 nOJACTaHoBoK:
( 1, (1 2), (I 3), (1 4), (2 3), (2 4', (3 4), (1 2), (3 4), (1 3) (2 4), (1 4) (2 3),
(2.5) ~(I 2 3), (1 3 2), (1 24), (1 42), (1 34), (1 4 3), (2 34), (2 4 3),
(1 2 3 4), (I 2 4 3), (I 3 2 4), (1 3 4 2), ( 1 4 2 3), (1 4 3 2).
3fuaonepemeirnaA rpynna ~24C0CT1iIT 113 12 nOiACTaHOBoX:
(20 (1, (1 2) (3 4), (I 3) (2 4), (1 4) (2 3), (1 2 3), (I 30 2), (1 2 41, (1 4 2),
I (1 3 4), (1 4 3), (2 30 4), (2 4 3).
Rpome roro, I"pyniia 04 CQ3jCPM1(HT Cne~yirniijyi nourpynry ilopurxma 8:
(2.7) 1, (1 32 4), (I4 2 3), (1 2) ~3 4), (t 3) (2 4), (I14) (2 3), (I 2), (3 4).
9ry rpynny MON(HO oxapa(TOp1H3oBallb, KaK COBiR01(1HCM 110AC~TaHOBOK, He mCHSIIOLLUIX B1upa)Keiniff xjx, -j x3x4.
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(2.8) 1, (1 2) (3 4), (1 3) (2 4), (1 4) (2 3).
Kpome Toro, 0:-4 coAepKHT HeCKOJIbKo 1(HK.3mtieCKHx rpynn, a Tam{~e rpynny
(2.9) 1, (1 2), (3 4), (1 2 ) (3 4).
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rpyen.
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(n = k-In1 + k2n,. + k n) OJACTaHoBOK, pa3JuaraIOLW~~IM Ha3 k.1 JHIK0B nopIAKa
u1, k, 1tHIK~oB nIOPSIIKa n.,.., k, LtHK7IOB nOP5IAKa nl8 rJUe fl1 >. > nl8.