Assignment:
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}.
Provide complete and step by step solution for the question and show calculations and use formulas.