▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Binary cartesian set product
▾ Binary relation
▾ Map
▾ Operation
▾ N-operation
▾ Binary operation
▾ Enclosed binary operation
▾ Groupoid
▾ Semigroup
▾ Monoid
▾ Group
▾ Subgroup
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}