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

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- Apr 20th 2009, 06:12 PMfunnyingahomomorphisms and kernels
Describe all group homomorphisms $\displaystyle f: \mathbb{Z} \ \rightarrow \ \mathbb{Z} $. Give their kernels and state which are injective and which are surjective.

- Apr 20th 2009, 06:40 PMAndres Perez
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.

- Apr 27th 2009, 09:42 AMfunnyinga
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.