Definition:Normal Subgroup

If $$G$$ is a group and $$H \le G$$, then $$H$$ is called a normal subgroup of $$G$$ if $$gH=Hg$$ for every $$g \in G$$. This is represented symbolically as $$H \triangleleft G$$.

One way to determine if a subgroup of $$G$$ is normal is by means of the normal subgroup test.