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> Let $H$ and $K$ be subgroups of a group $G$, $HK=KH$ and $H\cap K=\{1\}$. Prove that $$HK\cong H\times K.$$
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Can some one tell me how to prove this question? I have spent too much time in it, still have no idea? Can someone tell me how to prove it? I know from HK=KH,we can know HK is a subgroup, but I am still not sure how to prove it?