Brailovsky, L. V.; Freiman, G. A. On a product of finite subsets in a torsion-free group. (English) Zbl 0697.20019 J. Algebra 130, No. 2, 462-476 (1990). Let \(K\), \(M\) be finite subsets of a torsion-free group \(G\) such that \(| K|=k>1\), \(| M|=m>1\) and \(| KM|=k+m-1\). It is shown that there exist \(a,b,q\in G\) such that \(K=\{a,aq,...,aq^{k-1}\}\), \(M=\{b,qb,...,q^{m-1}b\}\). Reviewer: V.Ufnarovskij Cited in 1 ReviewCited in 11 Documents MSC: 20F05 Generators, relations, and presentations of groups 11B13 Additive bases, including sumsets 11P99 Additive number theory; partitions Keywords:cosets; finite subsets; torsion-free group × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Freiman, G. A.; Schein, B. M., Group and semigroup theoretic considerations inspired by inverse problems of the additive number theory, (Lecture Notes in Mathematics, Vol. 1320 (1988), Springer-Verlag: Springer-Verlag New York/Berlin), 121-140 · Zbl 0668.20023 [2] Kemperman, J. H.B, On complexes in a semigroup, Indag. Math., 18, 247-254 (1956) · Zbl 0072.25605 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.