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 and 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