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. I'm trying to get a better understanding of how to begin proofs. I'm always a little lost when trying to solve them. I 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? I wrote that α = τ_1 · · · τ_s = (τ_1 τ_s)(τ_1 τ_s-1)...(τ_1 τ_2) But does this qualify as a proof for showing that any l cycle can be written as a product of l-1 cycles? Even so, how does this make sense for s geq l -1? Sorry, I'm just trying to understand this more clearly.