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Symmetric Groups and Disjoint Cycles

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Suppose that τ in Sn fixes no symbol. Show that τ = μ^m for some n-cycle μ and positive integer m if and only if τ is the product of disjoint cycles of equal length.

I know that τ can be written as the product of disjoint cycles, but am not sure how to proceed from there.

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Symmetric groups and disjoint cycles are investigated. Products of disjoint cycles are determined.

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" ": If for some n-cycle and positive , we can assume that , then we consider the orbit of under ...

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