Normal subgroup of finitely generated group

This article describes a property that arises as the conjunction of a subgroup property: normal subgroup with a group property imposed on the ambient group: finitely generated group
View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup

Definition

Symbol-free definition

A subgroup of a group is termed a normal subgroup of finitely generated group if the whole group is a finitely generated group and the subgroup is a normal subgroup.

Relation with other properties

Stronger properties

• Normal subgroup of finite group
• Normal subgroup of slender group

Weaker properties

• Normal subgroup