Isomorph-normal characteristic subgroup of group of prime power order

This article describes a property that arises as the conjunction of a subgroup property: isomorph-normal characteristic 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 $P$ is termed an isomorph-normal characteristic subgroup of group of prime power order if $P$ is a group of prime power order and $H$ is an isomorph-normal characteristic subgroup: $H$ is an isomorph-normal subgroup of $P$ (every subgroup isomorphic to it is normal) and $H$ is a characteristic subgroup of $P$.

Relation with other properties

Stronger properties

• Isomorph-free subgroup of group of prime power order
• Subisomorph-containing subgroup of group of prime power order
• Characteristic maximal subgroup of group of prime power order

Weaker properties

• Characteristic subgroup of group of prime power order, characteristic subgroup
• Isomorph-normal subgroup of group of prime power order, isomorph-normal subgroup
• Normal subgroup of group of prime power order, normal subgroup
• Isomorph-normal coprime automorphism-invariant subgroup of group of prime power order, isomorph-normal coprime automorphism-invariant subgroup
  • Fusion system-relatively weakly closed subgroup
  • Sylow-relatively weakly closed subgroup