# 抽象代數-conjugate&normal subgroup

1.

Suppose that a is conjugate to b in a group G.

Show that C(a) is also conjugate to C(b) in G

2.

Show that if H and K are normal subgroups of a group G such that

H聯集K={e} , then hk=kh for all h屬於H and k屬於K

Update:

To 淡淡:

Update 2:

!!!

Rating

1. a conjugate to b in G <=> there exists g in G such that g a g^-1 = b

for all A in c(a) , i.e. aA=Aa, try to show gAg^-1 commute with b.

gAg^-1 b = g A (g^-1 b g) g^-1 = g A (a ) g^-1 = g a A g^-1

= g a g^-1 g A g^-1 =b g A g^-1. so we done.

我是物理系的學生，想嘗試修數學系純數的課

常常課本都覺得很有道理

但是一做習題就沒輒...

(你沒說我不知道原來我的問題都很基本....)