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Group Theory: Prove that any element σ in Sn which commutes with (1 , 2 , ... , r) is of the form σ = (1 , 2 , ... , r)^i τ where i = 0, 1 , 2 , ... , r , τ is a permutation leaving all of 1 , 2 , ... , r fixed.

Prove that any element σ in Sn which commutes with (1 , 2 , ... , r) is of the form σ = (1 , 2 , ... , r)^i τ
where i = 0, 1 , 2 , ... , r , τ is a permutation leaving all of 1 , 2 , ... , r fixed.

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Solution Summary

Commutativity of permutation groups is investigated. The solution is detailed and well presented.

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