Normal subgroup

Group theory

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In group theory, a branch of mathematics, a subgroup [math]\displaystyle{ N }[/math] of the group [math]\displaystyle{ G }[/math] is normal in [math]\displaystyle{ G }[/math] if and only if [math]\displaystyle{ \frac{1}{gng} \in N }[/math] for all [math]\displaystyle{ g \in G }[/math] and [math]\displaystyle{ n \in N }[/math].

The usual notation for this relation is [math]\displaystyle{ N \triangleleft G. }[/math]