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


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 definition
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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

Relation with other properties

Stronger properties