Sectionally AEP-subgroup

Definition
A subgroup $$H$$ of a group $$G$$ is termed sectionally AEP if there exists a homomorphism of groups:

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

such that for any automorphism $$\sigma$$ of $$H$$, $$\sigma$$ is the restriction to $$H$$ of $$\alpha(\sigma)$$.

Stronger properties

 * Weaker than::NSCFN-subgroup
 * Weaker than::Automorphism-faithful AEP-subgroup
 * Weaker than::Direct factor

Weaker properties

 * Stronger than::AEP-subgroup