Exercise 3.4.1 Let 7 € S₂ and suppose that o = (k₁ k₂ is also a j-cycle, and is given by kj) is a j-cycle. Prove that the conjugate of σ

by T 0 τστ = (T(K1) T(K₂) T(kj)). Further prove that if o' Sn is any other j-cycle, then o and o' are conjugate. Hint: For the second part, you should explicitly find a conjugating element T € Sn.