(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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