(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

None that I know of

3. 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.

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# Homework Help: Show the Symmetric group is generated by the set of transpositions (12) (n-1 n).

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