On the cardinality of sumsets in torsion‐free groups
Let A, B be finite subsets of a torsion‐free group G. We prove that, for every positive integer k, there is a c(k) such that if |B| ⩾ c(k), then the inequality |AB| ⩾ |A|+|B|+k holds unless a left translate of A is contained in a cyclic subgroup. We obtain c(k) < c0k6 for arbitrary torsion‐free g...
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| Veröffentlicht in: | The Bulletin of the London Mathematical Society 2012-10, Vol.44 (5), p.1034-1041 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let A, B be finite subsets of a torsion‐free group G. We prove that, for every positive integer k, there is a c(k) such that if |B| ⩾ c(k), then the inequality |AB| ⩾ |A|+|B|+k holds unless a left translate of A is contained in a cyclic subgroup. We obtain c(k) < c0k6 for arbitrary torsion‐free groups, and c(k) |
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| ISSN: | 0024-6093 1469-2120 |
| DOI: | 10.1112/blms/bds032 |