Abstract
AbstractWe prove Bogolyubov–Ruzsa-type results for finite subsets of groups with small tripling, |A3| ≤ O(|A|), or small alternation, |AA−1A| ≤ O(|A|). As applications, we obtain a qualitative analogue of Bogolyubov’s lemma for dense sets in arbitrary finite groups, as well as a quantitative arithmetic regularity lemma for sets of bounded VC-dimension in finite groups of bounded exponent. The latter result generalizes the abelian case, due to Alon, Fox and Zhao, and gives a quantitative version of previous work of the author, Pillay and Terry.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science
Reference39 articles.
1. A group version of stable regularity
2. Sur quelques propriétés arithmétiques des presque-périodes;Bogolioùboff;Ann. Chaire Phys. Math. Kiev,1939
3. On Jordan's theorem for complex linear groups
4. [29] Plünnecke, H. (1969) Eigenschaften und Abschätzungen von Wirkungsfunktionen, BMwF-GMD-22, Gesellschaft für Mathematik und Datenverarbeitung.
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献