# Solvable 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): solvable group

View a complete list of such conjunctions

## Contents

## Definition

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

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