Intermediately AEP-subgroup

Symbol-free definition
A subgroup of a group is termed an intermediately AEP-subgroup if it is an defining ingredient::AEP-subgroup in every intermediate subgroup.

Definition with symbols
A subgroup $$H$$ of a group $$G$$ is termed an intermediately AEP-subgroup if for every subgroup $$K$$ of $$G$$ containing $$H$$, $$H$$ is an AEP-subgroup of $$K$$. In other words, every automorphism of $$H$$ extends to an automorphism of $$K$$.

Stronger properties

 * Weaker than::Direct factor
 * Weaker than::Normal intermediately AEP-subgroup

Weaker properties

 * Stronger than::AEP-subgroup