# Locally nilpotent 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): locally nilpotent group

View a complete list of such conjunctions

## Definition

A subgroup of a group is termed a **locally nilpotent normal subgroup** if it is locally nilpotent as a group, and normal as a subgroup.

## Facts

- The subgroup generated by all locally nilpotent normal subgroups is the unique largest locally nilpotent normal subgroup of the group, and is termed the Hirsch-Plotkin radical of the group.