Small doubling in ordered nilpotent groups of class 2

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

doi:10.1016/j.ejc.2017.07.006

Small doubling in ordered nilpotent groups of class 2

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

School of Mathematical Sciences

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

5 Scopus citations

Abstract

The aim of this paper is to present a complete description of the structure of finite subsets S of torsion-free nilpotent groups of class 2 satisfying |S²|=3|S|−2. In view of results in [12], this gives a complete description of the structure of finite subsets with the above property in any torsion-free nilpotent group.

Original language	English
Pages (from-to)	87-95
Number of pages	9
Journal	European Journal of Combinatorics
Volume	67
DOIs	https://doi.org/10.1016/j.ejc.2017.07.006
State	Published - Jan 2018

Keywords

Finite subsets
Nilpotent groups
Ordered groups
Small doubling

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10.1016/j.ejc.2017.07.006

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title = "Small doubling in ordered nilpotent groups of class 2",

abstract = "The aim of this paper is to present a complete description of the structure of finite subsets S of torsion-free nilpotent groups of class 2 satisfying |S2|=3|S|−2. In view of results in [12], this gives a complete description of the structure of finite subsets with the above property in any torsion-free nilpotent group.",

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AU - Maj, Mercede

AU - Stanchescu, Yonutz V.

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AB - The aim of this paper is to present a complete description of the structure of finite subsets S of torsion-free nilpotent groups of class 2 satisfying |S2|=3|S|−2. In view of results in [12], this gives a complete description of the structure of finite subsets with the above property in any torsion-free nilpotent group.

KW - Finite subsets

KW - Nilpotent groups

KW - Ordered groups

KW - Small doubling

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Small doubling in ordered nilpotent groups of class 2

Abstract

Keywords

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