Symmetric subset

From Groupprops
Revision as of 15:31, 13 June 2007 by Vipul (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search
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