Let $G$ be a group and $H$ be a subgroup. $H$ is normal if it is closed under conjugation, i.e. for any $g\in G$ and for all $a\in H$,
\[\conj_g a = gag^{-1} \in H.\]
All subgroups of an abelian group are normal.
Let $G$ be a group and $H$ be a subgroup. $H$ is normal if it is closed under conjugation, i.e. for any $g\in G$ and for all $a\in H$,
\[\conj_g a = gag^{-1} \in H.\]
All subgroups of an abelian group are normal.