# Subgroup-closed group property

From Groupprops

This article defines a group metaproperty: a property that can be evaluated to true/false for any group property

View a complete list of group metaproperties

## Contents

## Definition

### Symbol-free definition

A group property is said to be **subgroup-closed** or **S-closed** if any subgroup of a group having the property also has the property.

### Definition with symbols

A group property is said to be **subgroup-closed** or **S-closed** if whenever satisfies property and is a subgroup of , must also satisfy property .