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Suppose n ≥ 3 is an integer. Prove that in Sn every even permutation is a...

Suppose n ≥ 3 is an integer. Prove that in Sn every even permutation is a product of cycles of length 3.

Hint: (a, b)(b, c) = (a, b, c) and (a, b)(c, d) = (a, b, c)(b, c, d).

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