ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation F9736 on D1394: Normal subgroup
F9736
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}