# Characteristic AEP-subgroup

From Groupprops

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This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: characteristic subgroup and AEP-subgroup

View other subgroup property conjunctions | view all subgroup properties

## Definition

A subgroup of a group is termed a **characteristic AEP-subgroup** if the homomorphism:

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