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    Nonisomorphic Abelian Groups

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    In each of parts (a) to (e) give the number of non-isomorphic abelian groups of the specified order - do not list the groups. (a) 100 (b) 576 (c) 1155 (d) 42875 (e) 2704.
    Prove that your answer is correct and list the groups in part (e).

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    Solution Preview

    For all the number of non-isomorphic abelian groups, we only need to know the order of this group. The solutions are as follows.
    (a) 100 = 2^2 * 5^2
    Then the number is 2 * 2 = 4
    (b) 576 = 2^6 * 3^2
    Then the number is 10 * 2 ...

    Solution Summary

    Nonisomorphic Abelian Groups are examined.