Symmetric subset

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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


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