Almost commuting permutations are near commuting permutations. (English) Zbl 1368.20025
Summary: We prove that the commutator is stable in permutations endowed with the Hamming distance, that is, two permutations that almost commute are near two commuting permutations. Our result extends to \(k\)-tuples of almost commuting permutations, for any given \(k\), and allows restrictions, for instance, to even permutations.
MSC:
| 20E26 | Residual properties and generalizations; residually finite groups |
| 20F65 | Geometric group theory |
| 43A07 | Means on groups, semigroups, etc.; amenable groups |
| 20F05 | Generators, relations, and presentations of groups |
| 20B30 | Symmetric groups |
| 15A27 | Commutativity of matrices |
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