1. The problem statement, all variables and given/known data Let α (alpha) all in S_n be a cycle of length l. Prove that if α = τ_1 · · · τ_s, where τ_i are transpositions, then s geq l − 1. 2. Relevant equations 3. The attempt at a solution What I was actually looking for is where to start with this proof. I don't want the answer, just a push in what direction I should be heading in. This is my trouble with proofs, I usually have no idea where to start. I've been told in the past to start with definitions of what is given to you in the question. A transposition is a permutation (bijective function of X onto itself) f, such that there exist i,j such that f(a_i) = a_j, f(a_j) = a_i and f(a_k) = a_k for all other k. I know that "l" is the length of the cycle. I also know that I want to somehow show that s is greater than l - 1 cycles. Does this mean I need to find out or show that any l cycle can be written as a product of l-1 cycles? Sorry, I'm just having a hard time with understanding this one. But I don't see how this helps me. Any suggestions?