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.
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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. 585–612DOI 10.4171/GGD/409