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    Z-Modules and Isomorphisms

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    (8) Prove that Hom_Z(Z/nZ,Z/mZ) is isomorphic to Z/(n,m)Z

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    We know, Z/nZ={0,1,...,n-1}, Z/mZ={0,1,...,m-1}. Let d=(n,m), then
    Z/dZ={0,1,...,d-1}. As a group, Z/nZ,Z/mZ,Z/dZ are all cyclic groups.
    So each homomorphism f from Z/nZ to Z/mZ is uniquely determined by f(1).
    Let f_k in ...

    Solution Summary

    Z-Modules and Isomorphisms are investigated.