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Math Help - finding homomorphism between cyclic groups

  1. #1
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    finding homomorphism between cyclic groups

    asked to find C_n to C_m,

    two possibilities:

    1, (n,m) =1,
    is it trivial ?

    2, what happens when (n,m) not = 1 ?
    got no idea
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  2. #2
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    \text{Hom}(\mathbb{Z}_n,\mathbb{Z}_m) = \{[x]_n\mapsto [kx]_m : m|kn \}
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