Small doubling in ordered nilpotent groups of class 2

被引：2

作者：

Freiman, Gregory A. ^{[1
]}

Herzog, Marcel ^{[1
]}

Longobardi, Patrizia ^{[2
]}

Maj, Mercede ^{[2
]}

Stanchescu, Yonutz V. ^{[3
,4
]}

机构：

[1] Tel Aviv Univ, Dept Math, Raymond & Beverly Sackler Fac Exact Sci, Tel Aviv, Israel

[2] Univ Salerno, Dipartimento Matemat, Via Giovanni Paolo 2, I-84084 Salerno, Italy

[3] Open Univ Israel, IL-43107 Raanana, Israel

[4] Afeka Acad Coll, IL-69107 Tel Aviv, Israel

来源：

EUROPEAN JOURNAL OF COMBINATORICS | 2018年 / 67卷

关键词：

Ordered groups; Finite subsets; Small doubling; Nilpotent groups; FREIMANS THEOREM; FINITE SUBSETS; ABELIAN-GROUP; SET ADDITION; PRODUCT;

D O I：

10.1016/j.ejc.2017.07.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 vertical bar S-2 vertical bar = 3 vertical bar S vertical bar - 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. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：87 / 95

页数：9

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