# Solvable 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): solvable group

View a complete list of such conjunctions

## Contents

## Definition

### Symbol-free definition

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

## Examples

VIEW: subgroups satisfying this property | subgroups dissatisfying property normal subgroup | subgroups dissatisfying property solvable groupVIEW: Related subgroup property satisfactions | Related subgroup property dissatisfactions