Theorem 6.9: Lets be a set. The set of all permutations of S, under the operation of composition of permutations, forms a group A(S) Proof: Lemma 6.1 implies that the rule of multiplication is well-defined associative the identity function from s to s is identity element The inverse permutation g of f is a permutation of s Theorem 6.9：Let S be a set. The set of all permutations of S, under the operation of composition of permutations, forms a group A(S).  Proof: Lemma 6.1 implies that the rule of multiplication is well-defined.  associative.  the identity function from S to S is identity element  The inverse permutation g of f is a permutation of S