Normal AEP-subgroup

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

For its use outside the wiki, please define the term when using it. If you are aware of an equivalent standard term, please leave a comment on the talk page
VIEW: Definitions built on this | Facts about this: (facts closely related to Normal AEP-subgroup, all facts related to Normal AEP-subgroup) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
Learn more about terminology local to the wiki | view a complete list of such terminology

This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: normal subgroup and AEP-subgroup
View other subgroup property conjunctions | view all subgroup properties

Definition

A subgroup of a group is termed a normal AEP-subgroup if it is a normal subgroup as well as an AEP-subgroup: a subgroup such that every automorphism of the subgroup can be extended to an automorphism of the whole group.

Relation with other properties

Stronger properties

• Direct factor
• NSCFN-subgroup
• Normal fully normalized subgroup
• Characteristic AEP-subgroup

Weaker properties

• Normal subgroup in which every subgroup characteristic in the whole group is characteristic
• Normal subgroup
• Subgroup in which every subgroup characteristic in the whole group is characteristic