I'm trying to understand a proof from Yahoo Answers of the following.
(a) Show that if $μ = (x_1, x_2, \dots, x_k) ∈ S_n$ is a $k$-cycle and $\sigma \in S_n$ is any permutation, then $\sigma μ \sigma^{−1}$ is the $k$-cycle $\sigma \mu \sigma^{−1} = (\sigma(x_1),\sigma(x_2), \dots ,\sigma(x_k))$.
(b) Using the above, find a necessary and sufficient condition for two permutations in $S_n$ to be conjugate to each other.
It does not look like part (a) is done very clearly. Can someone explain it?
Thanks