Normal intermediately AEP-subgroup

Definition
A subgroup of a group is termed a normal intermediately AEP-subgroup if it is both a normal subgroup and an intermediately AEP-subgroup: any automorphism of the subgroup can be extended to an automorphism for every intermediate subgroup containing it.

Stronger properties

 * Weaker than::Direct factor
 * Weaker than::Complete direct factor

Weaker properties

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