Coprime automorphism-invariant subgroup of group of prime power order

This article describes a property that arises as the conjunction of a subgroup property: coprime automorphism-invariant 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 (i.e., a finite $p$-group for some prime number $p$) $P$ is termed a coprime automorphism-invariant subgroup if it is invariant under all the $p'$-automorphisms, i.e., the automorphisms whose order is relatively prime to $p$.

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