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    Abelian groups

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    Let G be group of order 54
    a. If G is abelian, what groups can it be up to isomorphisms
    b. If G is nonabelian and the order of G is 24 and G is isomorphic to H x Z_3, what are the possibilities for H up to isomorphism
    c. If p and q are distinct primes, how many abelian groups are there of order p (square) q(fourth)?

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    Solution Summary

    This solution demonstrates how to solve the given problems regarding abelian groups.