Let G be a finite group and H be a normal subgroup of order 2. Then order if the center of G is
a) 0
b) 1
c) An even integer >=2
d) An odd integer >=3
I know a0 is not right. I think we have to use class eqn. but I dont know ho to proceed.
Prove: if a group has a normal subgroup of order 2 then this subgroup is central (i.e., it is contained in the group's center). ( hint: very easy proof: uses the fact that conjugate elements have the same order... )