Subgroup with canonical abelianization

Definition
A subgroup with canonical Abelianization is a subgroup satisfying the following property: any defining ingredient::inner automorphism of the whole group that sends the subgroup to itself, restricts to an defining ingredient::IA-automorphism of the subgroup.

Stronger properties

 * Weaker than::Central factor of normalizer
 * Weaker than::Central factor
 * Weaker than::Self-normalizing subgroup