invariant subgroup | normal group | self-conjugate subgroup

A normal subgroup is a subgroup that is fixed under conjugation by any element.

Let H be a subgroup of a group G. The similarity transformation of H by a fixed element x in G not in H always gives a subgroup. If x H x^(-1) = H for every element x in G, then H is said to be a normal subgroup of G, written H⊲G. Normal subgroups are also known as invariant subgroups or self-conjugate subgroup. All subgroups of Abelian groups are normal.

Abelian group | group | normal factor | normal series | quotient group | subgroup

college level