A group version of stable regularity. (24th October 2018)

• Record Type: Journal Article
• Authors: CONANT, G.; PILLAY, A.; TERRY, C.
• Is Part Of: Mathematical proceedings of the Cambridge Philosophical Society. Volume 168:Part 2(2020)
• Page Start: 405
• Page End: 413
• Publication Date: 2018-10-24
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1017/S0305004118000798
• Languages: English
• ISSNs: 0305-0041

Abstract

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 $\mathbb{F}_p$ .