On the structure of subsets of an orderable group with some small doubling properties

TL;DR

This paper characterizes the structure of certain subsets within non-abelian orderable groups that have small doubling properties, specifically when the size of their product set is exactly three times their size minus two.

Contribution

It provides a complete structural description of subsets with small doubling in non-abelian orderable groups, extending understanding beyond abelian cases.

Findings

Characterization of subsets with |S^2|=3|S|-2 in non-abelian orderable groups

Identification of structural properties of such subsets

Extension of small doubling theory to non-abelian orderable groups

Abstract

The aim of this paper is to present a complete description of the structure of subsets S of an orderable group G satisfying |S^2| = 3|S|-2 and <S> is non-abelian.