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Subsets with small sums in abelian groups. I: The Vosper property. (English) Zbl 0883.05065
This paper characterizes the finite subsets \(B\) in an abelian group \(G\) such that, for any finite subset \(A\) having at least two elements, \(|A + B|\geq\) min\((|G|-1, |A|+|B|)\). The approach uses graph-theoretic ideas on Cayley graphs, including the concepts of “fragments” and “atoms” in a graph (as in H. A. Jung [Math. Ann. 202, 307-320 (1973; Zbl 0239.05133)]). Applications are given to diagonal forms over finite fields and to characterizing Cayley graphs (or loop networks) of high connectivity.

05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C40 Connectivity
20D60 Arithmetic and combinatorial problems involving abstract finite groups
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