Finitely generated 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): finitely generated group
View a complete list of such conjunctions

Definition

A subgroup of a group is termed a finitely generated normal subgroup if it is normal as a subgroup and finitely generated as a group.

Relation with other properties

Stronger properties

• Finite normal subgroup

Weaker properties

• Normal closure of finite subset