Can you please show me the proof of this theorem?
" Every permutation under Sn where n>1 is a product of two cycles"
Clearly the identity can be expressed as and it is a product of 2-cycles. And since you know that every permutation of a finite set can be written as a cycle or as a product of disjoint cycles (proof?), every permutation can be expressed in the form:
then you will have: