# Automorphism-faithful AEP-subgroup

From Groupprops

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

View other subgroup property conjunctions | view all subgroup properties

## Definition

A subgroup of a group is termed an **automorphism-faithful AEP-subgroup** if for every automorphism of , there is a *unique* automorphism of whose restriction to is that particular automorphism.