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Let $G$ be a finite abelian group of order $n$ with identity $e$. If for all $a\in G$, $a^3=e$, then by induction on $n$, show that $n=3^k$ for some non-negative integer $k$.

I am competely stuck on this. Please help anybody.

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    Could you elaborate a bit on what results you have already seen? There are a lot of ways to show this, depending on how advanced results you have seen.2012-12-30
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    This sounds way too much like the group theory homework that Neptune has been posting in the past few minutes.2012-12-30
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    Yes indeed, Calvin. I suppose it is a rather widespread "trick"...2012-12-30

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