Small doubling in ordered groups: Generators and structure

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

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)585-612
Number of pages28
JournalGroups, Geometry, and Dynamics
Volume11
Issue number2
DOIs
StatePublished - 2017

Keywords

  • Inverse problems
  • Nilpotent groups
  • Ordered groups
  • Small doubling

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