Let $\sigma,\tau \in{S_n}$ such that $ \sigma \tau = \tau \sigma $. Let $\sigma = c_1c_2..c_i, \tau = C_1C_2...C_j$ be the decompositions in disjoint cycles of $\sigma, \tau$. Then, for any $k,l$, do $c_k$ and $C_l$ commute?

  • $\begingroup$ For some $k,l$ or for every $k,l$ ? $\endgroup$ – lhf Dec 13 '18 at 17:47

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