Groupes quotients

G H ⊂G
H2G G G/H
H G
n=|H|H G n
G
G G
Z Z/n
nSnZkk∈N
H K G H ∩K
K[K:H∩K]6[G:H]
K H K  H H  G K 6G
H K ⊂H G
H[G:H] = m g ∈G
16k6m gk∈H
HCG
π:G→G/H
Q ϕ :G→Q
Q G
K
G/H K
G K H
H1⊂G1H2⊂G2
H1H2H1×H2G1×G2
(G1×G2)/(H1×H2)∼
=G1/H1×G2/H2
H1ϕ:G1→G2
H2=ϕ(H1)H1∼
=H2G1/H1∼ =G2/H2
G1G2H1H2
G1/H1G2/H2
G H π :G→G/H
ϕ:G→KIm ϕ∼
=G/ Ker ϕ
K G K ∩H K π(K)
K/(K∩H)
KH := {k·h, k ∈K, h ∈H}G H
KH/H ∼
=K/(H∩K)
G/H
G H
K G H (G/H)/(K/H)∼
=
G/K

E k F ⊂E
G F E G ∼
=E/F
G Z(G)G/Z(G)
G
HCG H G/H G
H G
G= GLn(k)H= SLn(k)k
G= On(R)H= SOn(R)
G=Z/2×Z/4H=h(0,2)iH=h(1,2)iH=h(1,1)i
G= H8H=h−1iH=hii
G H H G
NHG x ∈G xHx−1=H
NHG H NH
NHG H
G D(G)G
ghg−1h−1g, h ∈G
D(G)G
G/D(G)
G ϕ :G→A
A G →G/D(G)
G/D(G)G G
SnD2n
D2nn H D2n
n H
H
n D2nD2n
2
H
D2n
G G
G×G→G G →G H
G H G
G/H