Homocyclic normal subgroup of finite group

This article describes a property that arises as the conjunction of a subgroup property: homocyclic normal subgroup with a group property imposed on the ambient group: finite group
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 is termed a homocyclic normal subgroup if it is a homocyclic normal subgroup (i.e., a homocyclic group and a normal subgroup) and the whole group is a finite group.

Relation with other properties

Stronger properties

• Cyclic normal subgroup of finite group

Weaker properties

• Finite-pi-potentially fully invariant subgroup
  • Finite-potentially fully invariant subgroup
  • Potentially fully invariant subgroup
  • Finite-pi-potentially characteristic subgroup