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    Permutation Groups : Cycles

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    Here's my problem:

    Let (i1, i2, . . . , ik) be a k-cycle (k less or equal to n) element of Sn and let sigma be an element of Sn.
    (i) Find a precise expression for sigma * (i1, i2, . . . , ik)* sigma-inverse.
    Hint: experiment a little, perhaps, then take a guess
    and prove it.

    (ii) Describe precisely the set {sigma * (1, 2, . . . , k) * sigma-inverse | sigma is an element of Sn}.

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