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Sumsets and subsets of Bohr sets in finite abelian groups. (Chinese. English summary) Zbl 1389.11029

Summary: Let \(G\) be a finite abelian group and \(A, B \subset G\). It is proved that there exist a Bohr set \(B\left({\Gamma, \delta} \right)\) and a constant \(D > 0\) such that \(A + B\) contains a translate of any set \(T \subset B(\Gamma, \delta)\) of size at most \(D\).

MSC:

11B13 Additive bases, including sumsets
20K01 Finite abelian groups
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