Submission date: 17 October 2017

Abstract:

We prove that, given ε > 0 and an integer k ≥ 1, there is an integer n such that the following holds. Suppose G is a sufficiently large finite group, and A ⊆ G is k-stable. Then there is a subgroup H of G, of index at most n, and Y ⊆ G, which is a union of left cosets of H, such that |A ∆ Y| ≤ ε|H|. It follows that, for any left coset C of H, either |C ∩ A| ≤ ε|H| or |C ࢨ A| ≤ ε|H|. This generalizes recent work of Terry and Wolf on vector spaces over F_p.

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Full text arXiv 1710.06309: pdf, ps.