Product of two subgroups

#group_theory

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 $H K = K H$ .

View

L A T E X

code

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 $HK=KH$.