Can you please show me the proof of this theorem?

" Every permutation under Sn where n>1 is a product of two cycles"

thanks (Giggle)

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- Sep 3rd 2010, 12:17 AMjherv05Permutation Groups
Can you please show me the proof of this theorem?

" Every permutation under Sn where n>1 is a product of two cycles"

thanks (Giggle)

- Sep 3rd 2010, 04:04 PMRoam
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: