Is there a general theory for elements of $S_n$ to commute? For example, it is common knowledge that if two elements are disjoint, then they commute. However, this is not a necessary condition. It is said here that cycles permute if and only if they are powers of one another or disjoint. This does not work for permutations that are not cycles, e.g. $(12)(34)$ and $(12)$.
2026-04-07 18:10:17.1775585417
Necessary and sufficient conditions for elements of $S_n$ to commute
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