# Symmetric subset

From Groupprops

This article defines a property of subsets of groups

View other properties of subsets of groups|View properties of subsets of abelian groups|View subgroup properties

## Contents

## Definition

### Symbol-free definition

A subset of a group is said to be **symmetric** if it satisfies the following equivalent conditions:

- The identity element lies inside the subset
- The inverse of any element in the subset also lies inside the subset