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## Homework Statement

**5.1:**Prove that S_n is generated by the set {(1 2), (3 4),...,(n-1 n)}

## Homework Equations

None that I know of

## The Attempt at a Solution

Any element in S_n can be written as a product of disjoint n-cycles. So now I need to show any n-cycle can be written as a product of 2-cycles. So if my cycle is (a1 ... ak) = (a1 a2)(a1 a3)...(a1 ak).

So now I've shown S_n can be generated by 2-cycles in general. I'm not sure how to extend this to say that S_n is generated by the set above.