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Math Help - finite abelian groups question

  1. #1
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    finite abelian groups question

    Let G be a finite group so that every subgroup is normal and has a complement (if H≤ G then there is a K ≤ G with G=H K and H ∩ K= <e>).
    a) show that G is abelian
    b) for any g ∈G, show o(g) is square free (i.e, a product of distinct primes)
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  2. #2
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    Re: finite abelian groups question

    This is easier if you know about the classification of Dedekind groups (every subgroup is normal). However, it also has a straight forward solution:

    finite abelian groups question-mhfgroups7.png
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