# Finitary permutation

From Groupprops

## Definition

Let be a set. A permutation on is termed a **finitary permutation** if the set of points such that is a finite subset of .

For a finite set, every permutation is finitary. For an infinite set, not all permutations are finitary. The finitary permutations form a proper subgroup of the symmetric group on , termed the finitary symmetric group on and denoted .