Show that, working in $Sn$ with $n \geq 4$, a transposition cannot be written as a product of 3-cycles.
With $n=4$, for instance, we cannot write them as a product of 3-cycles, but we can write them as a product of 2-cycles. Thus, transpositions cannot be written as a product of 3-cycles.
I am not sure how to prove this. Any help or suggestions would be greatly appreciated.