Small doubling in ordered groups: generators and structure

Published 8 Jan 2015 in math.NT, math.CO, and math.GR | (1501.01838v1)

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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