Question: 6) Let n 2. (a) Prove that Sn is generated by the transpositions (1 2), (1 3),...,(1 n). (b) Prove that Sn is generated by

6) Let n 2.

(a) Prove that Sn is generated by the transpositions (1 2), (1 3),...,(1 n).

(b) Prove that Sn is generated by the transpositions (1 2), (2 3),...,(n1 n).

(c) We consider the transposition = (1 2) and the cycle c = (1 2 3...n). Calculate cktc-k

(d) Deduce that Sn is generated by and c.

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