Exercise
Write (1,2,3,4,5) as a product of 3-cycles.
(1,2,5)(1,2,3)(1,2,4).
(1,2,5)(2,3,4).
(1,5,2)(5,4,3).
This product defines the permutation (1,3,2,4,5).
This is correct.
This product defines the permutation (5,4,3,2,1).