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For any subgroup of the group $G$, let $H^2$ denote the product $H^2=HH$. Prove that $H^2=H$.

This question seems simple but I do not know how can I prove.

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    Hint: Denote the unit element of $G$ as $1_G$. Then $1_G \in H$...2012-05-08
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    Use that $H$ is closed under multiplication and $1\in H$. | My bad @MattE!2012-05-08
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    @anon: Dear anon, It is stronger than that. Closure under multiplication implies that $H^2 \subset H$, but you need more to get equality. Regards,2012-05-08

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