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Math Help - finite abelian groups

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    finite abelian groups

    G finite abelian group
    1 subgroup of order d for each divisor d of |G|.
    Prove G cyclic.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by stumped765 View Post
    G finite abelian group
    1 subgroup of order d for each divisor d of |G|.
    Prove G cyclic.
    What if we proved the contrapositive. Suppose that G is not cyclic. Try constructing subgroups of G which are distinct but have the same order (hint: you're going to want to construct these subgroups to be cyclic groups [math}C_n,C_m[/tex] say with some prime p\mid m,n)
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