Product of two subgroups

Mar 14, 2025 10:28 PM

Let $G$ be a group, and $H, K$ be subgroups of $G$ . Let $H K = {h k ∣ h \in H, k \in K}$ denote the set product. Prove that $H K$ is a group if and only if $H K = K H$ .

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Let $G$ be a group, and $H, K$ be subgroups of $G$. Let $HK=\{hk\,\mid \, h\in H, k\in K\}$ denote the set product. Prove that $HK$ is a group if and only if $HK=KH$.