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