# Finitary symmetric group

From Groupprops

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphismTemplate:IAPS member

View a complete list of group propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

## Definition

A **finitary symmetric group** on a set is the group of all those permutations of the set that have finite support, viz permutations that fix all but finitely many elements. A group is said to be a **finitary symmetric group** if it is the finitary symmetric group over some set.