# Characteristic AEP-subgroup

## Contents

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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 $H$ of a group $G$ is termed a characteristic AEP-subgroup if the homomorphism:

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

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