Small doubling in ordered groups: generators and structure
Gregory A. Freiman, Marcel Herzog, Patrizia Longobardi, Mercede Maj,, Alain Plagne, Yonutz V. Stanchescu
TL;DR
This paper investigates the structure of subgroups generated by small doubling sets in ordered groups, extending classical results like Freiman's theorems to more general and non-abelian contexts.
Contribution
It provides new structural results and generalizations of Freiman's theorems for small doubling subsets in ordered groups, both abelian and non-abelian.
Findings
Generalized Freiman's 3k-3 and 3k-2 theorems
Precise subgroup structure descriptions
Extensions to non-abelian ordered groups
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.
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