Theorem 6.10: let s be a finite set with n elements. Then A(S) has n! elements. Definition 10: The group S, is the set of permutations of the first n natural numbers. The group is called the symmetric group on n letters, is called also the permutation group Theorem 6.10: Let S be a finite set with n elements. Then A(S) has n! elements.  Definition 10: The group Sn is the set of permutations of the first n natural numbers. The group is called the symmetric group on n letters, is called also the permutation group