$\alpha=(3412)(245)\in S_5$ and I have to 1) write this as a product of disjoint cycles, 2) write this as a product of transpositions.
1) I can do thing by following where the elements go in the two permutations. I obtain $\alpha=(21)(453)$ this seems to be correct.
2) How do I write this as a product of transpostions? I have trouble seeing how this is possible, seeing that $\alpha$ has a three length cycle within it.
How do I do 2)?