 Complement of a normal subgroup (source code)

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= Complement of a normal subgroup
{title2=$G=NH,\quad N\cap H=1$}

= Group complement
{synonym}

A group complement to a <normal subgroup> $N\triangleleft G$ is a subgroup $H$ with $G=NH$ and $N\cap H=1$. Projection identifies $H$ with $G/N$, and conjugation gives $G=N\rtimes H$. This is a subgroup notion, not the set-theoretic complement of $N$.

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