# Coprime automorphism-invariant normal subgroup of group of prime power order

From Groupprops

This article describes a property that arises as the conjunction of a subgroup property: coprime automorphism-invariant normal subgroup with a group property imposed on theambient group: group of prime power order

View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup

## Contents

## Definition

A subgroup of a group of prime power order is termed a **coprime automorphism-invariant normal subgroup** if it satisfies *both* these conditions:

- It is a normal subgroup of : in particular, it is a normal subgroup of group of prime power order.
- It is a coprime automorphism-invariant subgroup of : in particular, it is a coprime automorphism-invariant subgroup of group of prime power order.

## Relation with other properties

### Stronger properties

- Fusion system-relatively weakly closed subgroup
- Sylow-relatively weakly closed subgroup
- Isomorph-normal coprime automorphism-invariant subgroup of group of prime power order