# Automorphism-faithful normal 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 normal subgroup

View other subgroup property conjunctions | view all subgroup properties

## Definition

A subgroup of a group is termed an **automorphism-faithful normal subgroup** if it is both an automorphism-faithful subgroup and a normal subgroup of the whole group.

## Relation with other properties

### Stronger properties

- Centralizer-free normal subgroup:
`For full proof, refer: Normal and centralizer-free implies automorphism-faithful`