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Permutation Groups : Cycles

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}.

Solution Summary

Permutation groups are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who posted the question.