Задача 10.

* (Change of variables) Consider $a,c\in S_n$, and let $b=c^{−1}ac$. а) Show that if $a$ is given by $a={\left( \begin{smallmatrix}i_1 \ldots i_n \\ j_1 \ldots j_n\end{smallmatrix}\right)}$, then $b={\left( \begin{smallmatrix} c(i_1) \ldots c(i_n) \\ c(j_1) \ldots c(j_n) \end{smallmatrix}\right)}$. б) Show that if $a$ is given as a product of independent cycles $a = (i_1 \ldots i_k) (j_1 \ldots j_l) \ldots$, then $b=(c(i_1) \ldots c(i_k))(c(j_1)\ldots c(j_l)) \ldots $.