On the Bogolyubov-Ruzsa lemma
classification
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math.NT
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a-2aabelianbogolyubov-ruzsacontainscosetdimensionalfinitegroup
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Our main result is that if A is a finite subset of an abelian group with |A+A| < K|A|, then 2A-2A contains an O(log^{O(1)} K)-dimensional coset progression M of size at least exp(-O(log^{O(1)} K))|A|.
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