Sylow-正规化子属于群系$CF$的

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1、639o64:iiVol.39,No.419967ACTAMATHEMATICASINICAJuly,1996Sylow-C-.E6A59F)@5Jc(T/A,jjW630715)B<:kFmZWOgGO{{f(p)}oYHPzOgvFpm{{f(q)}
f(q),q=p,f(q)=

2、wg,q
=p,PzOp-YHPzgvNsa^gvFtb]1)kF_hygn~F,NfXNQ`p.ep-Sylow-SUn~Fp.~m“gG∈N.F(a^{FO[)OLxqVmQ`p,ep-Sylow-SUOFplMS~Gd2)gGsIZWOLxqVm

3、Q`p,ep-Sylow-SUsp-IZWf2-ea^lMS~GdiQ`p,gGOp-Sylowgujg;pMQKgOp-SylowgrRKGsB-g3)kGsB-g}gvFT~σ-Sylowpgvd~mG∈F,NfXNQ`p,GOp-Sylow-SUn~Fp;G∈N·F,NfXNQ`p,GOp-Sylow-SUOFpl
GdMS,/(YHPzgvSylow-SUIZWgσ-SylowpqH

4、[3p-3QZfnzn3ewmls

5、EF3g
d"{

6、[
3nDSy
zSylow3QZ(d!Syl

7、ow-QZ)3ewml4# M3uDO[1]2%{Sylow-QZpN~3N~O[2];[3];[4]kNp-Sylow-QZNp-~3N~[5]{

8、[Nk~3$oEe4Sylow-QZ3~.N(QO[6]HOBaer7y[7,7y7.23]NqHσ-SylowA6UF3$oEe4p-Sylow-QZ6Fp.OHO[5]3g
0qn7vUF,20ySylow-QZwtYsh3qH$oEeOmlXN

9、[FNsh3z{f(p)}n7v3UFpNzF/%3p-n7vU

10、NN~UX·Y3XzYv?"x1?2>11q(Q3?

11、J&g]NQ1994919%514Sylow-R[7;VF4}457FF>12,HNG3H3F-.HVH∩GF∼F/GF∈F,FFD4wH/H∩G=HGLH≤H∩G.>13,G

12、QSylowp-P,4“G∈Fp⇔G/CG(P)∈f(p)”.D4zO[8,xy2.1],b2Fp=1,>14,PNG3QSylowp-'P∩GG∈Fp.FpFpD4wNP∩G=1,L

13、]P×G.FpFp?tCG(P)≥G.;G=A,G=G/A,P=PA/A.4P∈S

14、ylpG.zG∈Fpaxy3,2G/CG(P∈f(p).z(

15、P

16、,

17、A

18、)=1a[9,7y7.9]CG(P)=CG(P)A/A=CG(P)/A,?G∼=G/A=G∈f(p).tCG(P)CG(P)/AC(P)zxy3,G∈Fp.G>15k~"

19、QSylow)'9>8`gσ,k~Nσ-SylowAD4,GNk~F(G)NFitting4G/F(G)N~'*>8p,1p

20、

21、G

22、,p

23、G/F(G)

24、,F(G)VGSylowp-P.PQF(G),NF(G)3B w'PG.&U9?

25、p

26、

27、G

28、,p

29、p

30、G/F(G)

31、,G

32、Q^+H≥

33、F(G),1

34、G:H

35、=p.ySH,2H

36、QSylowQ,'Q4p-Q4G3SylowtBL2QG,&U9p,H

37、QSylowp-P1,$

38、P1G.49GSylow[10]P,p

39、@3^+P1QGw'GNsh.G

40、SylowA."

41、QSylow>16&UF#oqG3p-Sylow-QZ6Fp,m

42、GNp-sh.G3p-Sylow-QZ3Fp.(QG0Gpp-shD4&UG3p-Sylow-QZ3Fp-.N1,p-Sylow-QZ6Fp,zc,2GNp-sh,p-Sylow-

43、QZNG(P)3Fp-.A
=1,1

44、(Qp-P∩A.'P∩A
=1,zxy1,G

45、Qp-P1.SG/P12G/P1Np-sh)'GNp-sh'p-Sylow-QZNG(P),

46、P∩A=1.zxy4,2NG(P)∈Fp.zc,Ee$2GNp-sh2+2*11,UF#X

47、Ee(∆)q6F,.j.9pp-Syl