Homomorph-containing subgroup of finite group

This article describes a property that arises as the conjunction of a subgroup property: homomorph-containing 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 homomorph-containing subgroup of finite group if the whole group is a finite group and the subgroup is a homomorph-containing subgroup of it.

Relation with other properties

Stronger properties

• Variety-containing subgroup of finite group
  • Normal Sylow subgroup
  • Normal Hall subgroup
  • Subgroup of finite cyclic group

Weaker properties

• Isomorph-free subgroup of finite group
• Fully invariant subgroup of finite group
• Characteristic subgroup of finite group
• Normal subgroup of finite group