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Math Help - homomorphisms and kernels

  1. #1
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    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.
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  2. #2
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    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.
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  3. #3
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    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.
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