Almost commuting permutations are near commuting permutations

Abstract

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.

Corrected the definition of the Loeb space; more details in the proof of the main result, Journal of Functional Analysis, Available online 2015

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• Limits of Hypergraphs, Removal and Regularity Lemmas. A Non-standard Approach
• Almost commuting matrices with respect to normalized Hilbert-Schmidt norm
• A Hilbert-Schmidt analog of Huaxin Lin's Theorem
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