JournalsggdVol. 11, No. 2pp. 585–612

Small doubling in ordered groups: generators and structure

  • Gregory A. Freiman

    Tel Aviv University, Israel
  • Marcel Herzog

    Tel Aviv University, Israel
  • Patrizia Longobardi

    Università di Salerno, Fisciano (Salerno), Italy
  • Mercede Maj

    Università di Salerno, Fisciano (Salerno), Italy
  • Alain Plagne

    Ecole polytechnique, Palaiseau, France
  • Yonutz V. Stanchescu

    The Open University of Israel, Raanana, and Afeka Academic College, Tel Aviv, Israel
Small doubling in ordered groups: generators and structure cover
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Abstract

We prove several new results on the structure of the subgroup generated by a small doubling subset of an ordered group, abelian or not. We obtain precise results generalizing Freiman’s 3k33k-3 and 3k23k-2 theorems in the integers and several further generalizations.

Cite this article

Gregory A. Freiman, Marcel Herzog, Patrizia Longobardi, Mercede Maj, Alain Plagne, Yonutz V. Stanchescu, Small doubling in ordered groups: generators and structure. Groups Geom. Dyn. 11 (2017), no. 2, pp. 585–612

DOI 10.4171/GGD/409