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Math Help - group order problem...

  1. #1
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    group order problem...

    Q:Let G be a finite abelian group of order n with identity e,If for all a belongs to G,a^3=e then by induction on n show that n=3^k for some non negative integer k??
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  2. #2
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    Quote Originally Posted by Mathventure View Post

    Q:Let G be a finite abelian group of order n with identity e,If for all a belongs to G,a^3=e then by induction on n show that n=3^k for some non negative integer k??
    Hint: to complete the induction choose any e \neq a \in G and apply the induction hypothesis to the quotient group \frac{G}{<a>}.
    Last edited by NonCommAlg; April 22nd 2009 at 12:04 AM.
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