(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.

Expert Solution

Colby Messinger answered 2 years ago

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