Finite normal subgroup

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

Relation with other properties

Stronger properties

• Normal subgroup of prime order
• Finite central subgroup
• Finite characteristic subgroup

Weaker properties

• Amalgam-characteristic subgroup: For full proof, refer: Finite normal implies amalgam-characteristic
• Finitely generated normal subgroup
• Normal closure of finite subset
• Finite subnormal subgroup

Related properties

• Normal subgroup of finite index