# Coprime 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: coprime automorphism-faithful subgroup and normal subgroup

View other subgroup property conjunctions | view all subgroup properties

## Contents

## Definition

### Symbol-free definition

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

## Relation with other properties

### Stronger properties

- Self-centralizing normal subgroup:
`For full proof, refer: Normal and self-centralizing implies coprime automorphism-faithful` - Coprime automorphism-faithful characteristic subgroup
- Automorphism-faithful normal subgroup
- Automorphism-faithful characteristic subgroup
- Centralizer-free normal subgroup
- Centralizer-free characteristic subgroup