Prove the following in $S_n$:
Let $\alpha = (a_1,a_2,\ldots,a_s)$ be a cycle and let $\pi$ be a permutation in $S_n$. Then $\pi\alpha\pi^{-1}$ is the cycle $(\pi(a_1),\ldots,\pi(a_s)).$
I'm not sure where to even start.
2026-04-09 03:49:29.1775706569
Conjugate cycles
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Hint
Let $\sigma=\pi\alpha\pi^{-1}$. Calculate $\sigma(\pi(a_k))$.