Let f be an r-cycle in $S_n$. Given any $h \in S_n$, show that $hfh^{-1} = (h(x_1), h(x_2), \dots, h(x_r))$

The problem: let $(x_1, x_2, …, x_r)$ be an r-cycle in $S_n$. Show that for every $h \in S_n$, $h \circ (x_1, x_2, \ldots, x_r) \circ h^{-1} = (h(x_1), h(x_2), \ldots, h(x_r))$

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