# Math Help - homomorphisms and kernels

1. ## homomorphisms and kernels

Describe all group homomorphisms $f: \mathbb{Z} \ \rightarrow \ \mathbb{Z}$. Give their kernels and state which are injective and which are surjective.

2. the homomorphism are completely determined by the image of 1 (why?), so put f(1)=n for some n and see what happens with the questions you have.

3. Its probably a really obvious solution, but I just can't think how to PROVE this. Its really annoying, I'm no good at this branch of mathematics and I need to be walked through. I'm not as mathematically inclined as the majority of other members on this site and I really need help.