Finite fully invariant subgroup

This article describes a property that arises as the conjunction of a subgroup property: fully invariant subgroup with a group property (itself viewed as a subgroup property): finite group
View a complete list of such conjunctions

Definition

A subgroup of a group is termed a finite fully invariant subgroup if it is finite as a group and is a fully invariant subgroup of the whole group.

Examples

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

Relation with other properties

Stronger properties

• Fully invariant subgroup of finite group

Weaker properties

• Finite strictly characteristic subgroup
• Finite injective endomorphism-invariant subgroup
• Finite characteristic subgroup
• Finite normal subgroup