I know the order of the product of disjoint cycles is their lcm. If both cycles are the same length, is this the order of their product or is lcm(x,x) not equal to x?
2026-03-27 13:03:34.1774616614
Order of product of disjoint cycles
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We do have $\operatorname{lcm}(x,x)=x$. And we have that the order of the product of two disjoint cycles, both of length $x$, is equal to $x$. This is exactly as you say it should be.