# Math Help - Is the image always a normal subgroup?

1. ## Is the image always a normal subgroup?

There is a homomorphism between G and G'. Does the image of the homomorphism always give a normal subgroup?

My thought is not always, because the homomorphism is not a bijective map. But how do I find a counterexample for this?

2. As an easy example take f: Z_2 --> S_3, f(a):= (12) , where Z_2 = {1,a}.

Tonio