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Math Help - Nonabelian group of order p^3 (2)

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    Nonabelian group of order p^3 (2)

    [Hungerford, p99 Q8]

    Let p be an odd prime. Prove that there are, at most, two nonabelian groups of order p^{3}.

    One has generators a,b satisfying  |a|=p^{2}; |b|=p; b^{-1}ab=a^{1+p}.
    The other has generators a,b,c satisfying |a|=|b|=|c|=p; c=a^{-1}b^{-1}ab; ca=ac; cb=bc.
    Last edited by aliceinwonderland; November 18th 2008 at 08:09 PM.
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