Normal subgroups with trivial intersection

Mar 18, 2025 5:32 PM

Let $G$ be a group and $H, K ⊴ G$ be normal subgroups with $H \cap K = {e}$ . Show that each element in $H$ commutes with every element in $K$ .

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Let $G$ be a group and $H,K\mathrel{\unlhd}G$ be normal subgroups with $H\cap K=\{e\}$. Show that each element in $H$ commutes with every element in $K$.