Geodesic
Small doubling in ordered groups: generators and structure
Gregory A. Freiman1 ; Marcel Herzog1 ; Patrizia Longobardi2 ; Mercede Maj2 ; Alain Plagne3 ; Yonutz V. Stanchescu4
1Tel Aviv University, Israel
2Università di Salerno, Fisciano (Salerno), Italy
3Ecole polytechnique, Palaiseau, France
4The Open University of Israel, Raanana, and Afeka Academic College, Tel Aviv, Israel
Groups, geometry, and dynamics, Tome 11 (2017) no. 2, pp. 585-612

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DOI

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 3k−3 and 3k−2 theorems in the integers and several further generalizations.
DOI : 10.4171/ggd/409
Classification : 11-XX, 20-XX
Mots-clés : Inverse problems, small doubling, nilpotent groups, ordered groups

Gregory A. Freiman  1   ; Marcel Herzog  1   ; Patrizia Longobardi  2   ; Mercede Maj  2   ; Alain Plagne  3   ; Yonutz V. Stanchescu  4

1 Tel Aviv University, Israel
2 Università di Salerno, Fisciano (Salerno), Italy
3 Ecole polytechnique, Palaiseau, France
4 The Open University of Israel, Raanana, and Afeka Academic College, Tel Aviv, Israel 
Gregory A. Freiman; Marcel Herzog; Patrizia Longobardi; Mercede Maj; Alain Plagne; Yonutz V. Stanchescu. Small doubling in ordered groups: generators and structure. Groups, geometry, and dynamics, Tome 11 (2017) no. 2, pp. 585-612. doi: 10.4171/ggd/409
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     author = {Gregory A. Freiman and Marcel Herzog and Patrizia Longobardi and Mercede Maj and Alain Plagne and Yonutz V. Stanchescu},
     title = {Small doubling in ordered groups: generators and structure},
     journal = {Groups, geometry, and dynamics},
     pages = {585--612},
     year = {2017},
     volume = {11},
     number = {2},
     doi = {10.4171/ggd/409},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/409/}
}
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