# Coprime automorphism-invariant 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 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

## Definition

A subgroup of a group of prime power order (i.e., a finite -group for some prime number ) is termed a **coprime automorphism-invariant subgroup** if it is invariant under all the -automorphisms, i.e., the automorphisms whose order is relatively prime to .

## Relation with other properties

### Stronger properties

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