\begin{definition}[Definition:Normal Subgroup/Notation]
The statement that $N$ is a normal subgroup of $G$ is represented symbolically as $N \lhd G$.
A normal subgroup is often represented by the letter $N$, as opposed to $H$ (which is used for a general subgroup which may or may not be normal).
To use the notation introduced in the definition of the conjugate:
:$N \lhd G \iff \forall g \in G: N^g = N$
Category:Definitions/Normality in Groups
\end{definition}