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    Kernel and Homomorphism

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    Here's my problem:

    If A and B are subsets of a group G, define
    AB = {ab | a 2 A, b 2 B}. Now suppose phi: G -> G0 is a homomorphism of groups and N = Ker(phi) is its kernel.

    (i) If H is a subgroup of G, show that HN = NH. (Warning: this is an equation of sets; proceed
    accordingly; do not assume that G is abelian.)

    (ii) Show that phi-inverse[phi[H]] = HN.


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    Solution Summary

    Kernels and Homomorphisms are investigated. The solution is detailed and well presented.