Quantitative structure of stable sets in arbitrary finite groups

@article{Conant2021QuantitativeSO,
  title={Quantitative structure of stable sets in arbitrary finite groups},
  author={Gabriel Conant},
  journal={Proceedings of the American Mathematical Society},
  year={2021}
}
  • G. Conant
  • Published 6 April 2020
  • Mathematics
  • Proceedings of the American Mathematical Society
We show that a $k$-stable set in a finite group can be approximated, up to given error $\epsilon>0$, by left cosets of a subgroup of index $\epsilon^{\text{-}O_k(1)}$. This improves the bound in a similar result of Terry and Wolf on stable arithmetic regularity in finite abelian groups, and leads to a quantitative account of work of the author, Pillay, and Terry on stable sets in arbitrary finite groups. We also prove an analogous result for finite stable sets of small tripling in arbitrary… 
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