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$\begingroup$

Is this true?

If $G$ is a group of size $n$, and $X$ is a non-empty subset of $G$ then $X^n$ is a subgroup of $G$?

By $X^n$ I mean the set of all products of length $n$ from $X$.

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    Welcome here. :)2012-10-13
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    Also posted to MathOverflow, http://mathoverflow.net/questions/109590/the-powers-of-non-empty-subset-of-a-group-that-generate-a-subgroup --- with no notification to either site. Not good.2012-10-14

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