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Let $\sigma=(i_1\; i_2\;\cdots \;i_k)$ be a $k$-cycle, for some $k\leq n$. Show that $(i_1\; i_2\;\cdots \;i_k)=(i_1\; i_2\;\cdots \;i_{k-1})(i_{k-1}\;i_{k})$.

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