# Symmetric subset

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

This article is about a standard (though not very rudimentary) definition in group theory. The article text may, however, contain more than just the basic definitionVIEW: Definitions built on this | Facts about this: (factscloselyrelated to Symmetric subset, all facts related to Symmetric subset) |Survey articles about this | Survey articles about definitions built on thisVIEW RELATED: Analogues of this | Variations of this | Opposites of this |

View a complete list of semi-basic definitions on this wiki

## Contents

## Definition

### Symbol-free definition

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

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