Description: Define the symmetric group on set x . We represent the group as the
set of one-to-one onto functions from x to itself under function
composition, and topologize it as a function space assuming the set is
discrete. This definition is based on the fact that a symmetric group
is a restriction of the monoid of endofunctions. (Contributed by Paul
Chapman, 25-Feb-2008)(Revised by AV, 28-Mar-2024)