Characteristic AEP-subgroup

Definition
A subgroup $$H$$ of a group $$G$$ is termed a characteristic AEP-subgroup if the homomorphism:

$$\operatorname{Aut}(G) \to \operatorname{Aut}(H)$$

that sends an automorphism of $$G$$ to its restriction to $$H$$ is well-defined (i.e., every automorphism of $$G$$ does restrict to an automorphism of $$H$$) and surjective (i.e., every automorphism of $$H$$ arises as the restriction of an automorphism of $$G$$).

Stronger properties

 * Weaker than::Characteristic direct factor
 * Weaker than::Normal Sylow subgroup
 * Weaker than::Normal Hall subgroup

Weaker properties

 * Stronger than::Characteristic subgroup in which every subgroup characteristic in the whole group is characteristic
 * Stronger than::Normal AEP-subgroup
 * Stronger than::Characteristic subgroup
 * Stronger than::AEP-subgroup