# Math Help - Abstract - Homomorphism

1. ## Abstract - Homomorphism

Hi,

Can anybody help with the following questions please?

1. Find the homomorphic image of the group S3.

2. Find two nonisomorphic extensions of Z 4 by Z 2.

Can you explain any answers please as I'm finding it hard to get my head around homomorphisms?

Thanks.

2. Originally Posted by jackiemoon

1. Find the homomorphic image of the group S3.
Remember that the homomorphic image of $S_3$ is isomorphic to $S_3$ modulo the kernel of the homomorphism. Since the kernel must be a normal subgroup of $S_3$ it means that the kernel is either $\{ e\}, A_3, S_3$ and so the homomorphic image is either $S_3, \mathbb{Z}_2, \text{ or }\mathbb{Z}_1$.

2. Find two nonisomorphic extensions of Z 4 by Z 2.
I am not sure what you mean by this?