Almost normal subgroup

Symbol-free definition
A subgroup of a group is said to be almost normal if it satisfies the following equivalent conditions:


 * 1) Its defining ingredient::normalizer has finite index in the whole group.
 * 2) It is a normal subgroup of a subgroup of finite index in the whole group.
 * 3) It has only finitely many defining ingredient::conjugate subgroups.

Related properties

 * Nearly normal subgroup

Facts
Every subgroup of a group is almost normal if and only if the center has finite index, or equivalently, if the inner automorphism group of the group is finite.