Definition:Normal Subgroup/Notation

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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:

$N \lhd G \iff \forall g \in G: N^g = N$