ThmDex – An index of mathematical definitions, results, and conjectures.
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Definition D1394
Normal subgroup
Formulation 1
Let $G$ be a D22: Group such that
(i) $H$ is a D496: Subgroup of $G$
Then $H$ is a normal subgroup of $G$ if and only if \begin{equation} \forall \, g \in G : \forall \, h \in H : g h g^{-1} \in H \end{equation}