# Normal subgroup of finitely generated group

From Groupprops

This article describes a property that arises as the conjunction of a subgroup property: normal subgroup with a group property imposed on theambient 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

## Contents

## 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.