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. Thanks to a result by G.A. Freiman, M. Herzog, P. Longobardi, M. Maj, A. Plagne, Y.V. Stanchescu, (see Small doubling in ordered groups: generators and structure, Groups, geometry and dynamics, 11(2), 2017, 585-612) this give a complete description of the structure of finite subsets with this property of any torsion-free nilpotent group.
"Small doubling in ordered nilpotent groups of class 2"
LONGOBARDI, Patrizia;MAJ, Mercede;
2018
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. Thanks to a result by G.A. Freiman, M. Herzog, P. Longobardi, M. Maj, A. Plagne, Y.V. Stanchescu, (see Small doubling in ordered groups: generators and structure, Groups, geometry and dynamics, 11(2), 2017, 585-612) this give a complete description of the structure of finite subsets with this property of any torsion-free nilpotent group.File in questo prodotto:
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Small-doubling-in-ordered-nilpotent-groups-of-class-2 .pdf
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