Abstract Algebra #50 please

If o is a cycle Show that Sn is generated by ((1, 2), (1, 2, 3, . .., n)). [Hint: Show that as r varies. (1, 2,3. ....n) (1. 2) (1. 2. 3. . . . . n)"- gives all the transpositions (1, 2), (2, 3), (3, 4), . . . . (n - 1, n). (n. 1). Then show that any transposition is a product of some of these transpositions and use Theorem 8.15.]