Automorphism-faithful AEP-subgroup

Definition
A subgroup $$H$$ of a group $$G$$ is termed an automorphism-faithful AEP-subgroup if for every automorphism of $$H$$, there is a unique automorphism of $$G$$ whose restriction to $$H$$ is that particular automorphism.

Weaker properties

 * Stronger than::Sectionally AEP-subgroup
 * Stronger than::AEP-subgroup