Article contents
A group version of stable regularity
Published online by Cambridge University Press: 24 October 2018
Abstract
We prove that, given ε > 0 and k ≥ 1, there is an integer n such that the following holds. Suppose G is a finite group and A ⊆ G is k-stable. Then there is a normal subgroup H ≤ G of index at most n, and a set Y ⊆ G, which is a union of cosets of H, such that |A △ Y| ≤ε|H|. It follows that, for any coset C of H, either |C ∩ A|≤ ε|H| or |C \ A| ≤ ε |H|. This qualitatively generalises recent work of Terry and Wolf on vector spaces over $\mathbb{F}_p$.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 168 , Issue 2 , March 2020 , pp. 405 - 413
- Copyright
- Copyright © Cambridge Philosophical Society 2018
Footnotes
Supported by NSF grants DMS-1360702 and DMS-1665035.
References
REFERENCES
- 10
- Cited by