- #1
hsong9
- 80
- 1
Homework Statement
If H is a normal subgroup of G and |H| = 2, show that H is a subgroup of Z(G).
Is this true when |H| = 3?
The Attempt at a Solution
Since H is a normal subgroup of G and |H| = 2 = {1,a},
a in Z(G), also aa = a2 = 1 in Z(G)
aa-1 = a in Z(G). Therefore H is a subgroup of Z(G).
I am not sure my approach is correct.
and I have no idea next question when |H| =3, is it false? why??