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