Normal subgroup

Subgroup invariant under conjugation

In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation by members of the group of which it is a part. In other words, a subgroup N {\displaystyle N} of the group G {\displaystyle G} is normal in G {\displaystyle G} if and only if g n g − 1 ∈ N {\displaystyle gng^{-1}\in N} for all g ∈ G {\displaystyle g\in G} and n ∈ N . {\displaystyle n\in N.} The usual notation for this relation is N ◃ G .

From Wikipedia, under CC BY-SA. More on occurri.