When a given set is finite it is clear. I'm asking the general case.
Let $X$ is an arbitrary set.
Let $\sigma,\tau$ be disjoint cycles on $X$.
Then do they commute?
2026-04-09 16:33:02.1775752382
Do disjoint cycles commute?
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Yes. Disjoint cycles always commute. Ask yourself this- what happens when you try to compose the two cycles? You can't simplify them further regardless of the order in which you compose them. Hence, you see commutativity.