# Nilpotent characteristic subgroup

From Groupprops

This article describes a property that arises as the conjunction of a subgroup property: characteristic subgroup with a group property (itself viewed as a subgroup property): nilpotent group

View a complete list of such conjunctions

## Contents

## Definition

A subgroup of a group is termed a **nilpotent characteristic subgroup** if it is characteristic as a subgroup and nilpotent as a group.

For a finite group, this is equivalent to being a characteristic subgroup contained inside the Fitting subgroup.