When we multiply cycles, do we keep multiplying until we get two disjoint cycles? Or is the final product supposed to be obtained in one step?
An example is
α=(1 2 3)(4 5)(1 6 7 8 9)(1 5)
= (1 4 5 6 7 8 9)(2 3 1 4 5 6 7 8 9)
= (1 5 7 9 2 3 4 6 8)
Is this right?