(i) | $H$ is a D496: Subgroup of $G$ |

**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}

▾ 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

▾ 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

Formulation 1

Let $G$ be a D22: Group such that

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}

(i) | $H$ is a D496: Subgroup of $G$ |