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

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

Relation with other properties

Stronger properties

• Gyro-twisted subgroup
• Subgroup