Almost commuting permutations are near commuting permutations
  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. 
Goulnara Arzhantseva and Liviu Paunescu
math.GR