G A, B ‚" G AB = {ab : a " A, b " B}
|AB| e" max(|A| , |B|)
H G H G
An Sn n " N
H G H NH =
{x " G : xHx-1 = H} NH < G H NH G
(G : NH) H
G
pn p
p
m mZ = {mx : x " Z}
(Z, +)
m H f : Z H
mZ
G N < H < G H G N G
N H G/H (G/N)/(H/N)
f : G/N G/H
N G H < G
HN < G
N HN
H )" N H (HN)/N H/(H )" N)
f : H HN/N