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

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 the ambient 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 $H$ of a group of prime power order $P$ is termed a coprime automorphism-invariant normal subgroup if it satisfies both these conditions:

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

Weaker properties

• Normal subgroup of group of prime power order
• Coprime automorphism-invariant subgroup of group of prime power order