Fully invariant subgroup of finite group

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

Examples

VIEW: subgroups satisfying this property | subgroups dissatisfying property fully invariant subgroup | subgroups whose group part dissatisfies property finite group
VIEW: Related subgroup property satisfactions | Related subgroup property dissatisfactions

Relation with other properties

Stronger properties

• Homomorph-containing subgroup of finite group
• Normal Sylow subgroup
• Normal Hall subgroup

Weaker properties

• Characteristic subgroup of finite group
• Normal subgroup of finite group