Prove that Sn is generated by {(i i + 1) I 1 < i < n - 1}.

Expert Solution

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Colby Messinger answered 1 year ago

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

(a) Prove that Sn is generated by the elements in the set {(i i+1) : 1≤i≤n}. [Hint: Consider conjugates, for example (2 3) (1 2) (2 3)−1.] (b) ProvethatSn isgeneratedbythetwoelements(12)and(123...n) for n ≥ 3. (c) Prove that H = 〈(1 3), (1 2 3 4)〉 is a proper subgroup of S4.

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Question

Prove that Sn is generated by {(i i + 1) I 1 < i < n - 1}.

Solutions

Expert Solution

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