# Finitely generated normal subgroup

From Groupprops

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

## Contents

## 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.