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  3. (a) prove that sn is generated by the elements in

(a) Prove that Sn is generated by the elements in the set {(i i+1) : 1≤i≤n}. [Hint:...

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Advance Math

(a) Prove that Sn is generated by the elements in the set {(ii+1) : 1≤i≤n}.

[Hint: Consider conjugates, for example (2 3) (1 2) (23)−1.]

(b) ProvethatSn isgeneratedbythetwoelements(12)and(123...n) forn ≥ 3.

(c) Prove that H = 〈(1 3), (1 2 3 4)〉 is a proper subgroup ofS4.

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