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A group version of stable regularity

  • G. CONANT (a1), A. PILLAY (a1) and C. TERRY (a2)

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 AG is k-stable. Then there is a normal subgroup HG of index at most n, and a set YG, which is a union of cosets of H, such that |AY| ≤ε|H|. It follows that, for any coset C of H, either |CA|≤ ε|H| or |C \ A| ≤ ε |H|. This qualitatively generalises recent work of Terry and Wolf on vector spaces over $\mathbb{F}_p$ .

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Supported by NSF grants DMS-1360702 and DMS-1665035.

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A group version of stable regularity

  • G. CONANT (a1), A. PILLAY (a1) and C. TERRY (a2)

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