A group isomorphic to an internal direct product

Suppose $G$ is a group that contains normal subgroups $H, K ⊴ G$ with $H \cap K = {e}$ and $H K = G$ . Prove that $G ≅ H \times K$ .

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Suppose $G$ is a group that contains normal subgroups $H,K\unlhd G$ with $H\cap K=\{e\}$ and $HK=G$. Prove that $G\cong H\times K$.