Small doubling in ordered groups: Generators and structure

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

doi:10.4171/GGD/409

Small doubling in ordered groups: Generators and structure

Gregory A. Freiman
, Marcel Herzog
, Patrizia Longobardi
, Mercede Maj
, Alain Plagne
, Yonutz V. Stanchescu

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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 3k 3 and 3k 2 theorems in the integers and several further generalizations.

Original language	English
Pages (from-to)	585-612
Number of pages	28
Journal	Groups, Geometry, and Dynamics
Volume	11
Issue number	2
DOIs	https://doi.org/10.4171/GGD/409
State	Published - 2017

Keywords

Inverse problems
Nilpotent groups
Ordered groups
Small doubling

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10.4171/GGD/409

Cite this

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title = "Small doubling in ordered groups: Generators and structure",

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 3k 3 and 3k 2 theorems in the integers and several further generalizations.",

keywords = "Inverse problems, Nilpotent groups, Ordered groups, Small doubling",

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note = "Publisher Copyright: {\textcopyright} European Mathematical Society.",

year = "2017",

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AU - Freiman, Gregory A.

AU - Herzog, Marcel

AU - Longobardi, Patrizia

AU - Maj, Mercede

AU - Plagne, Alain

AU - Stanchescu, Yonutz V.

N1 - Publisher Copyright: © European Mathematical Society.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Inverse problems

KW - Nilpotent groups

KW - Ordered groups

KW - Small doubling

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SP - 585

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IS - 2

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Small doubling in ordered groups: Generators and structure

Abstract

Keywords

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