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Approximate groups. I The torsion-free nilpotent case

Part of: Sequences and sets

Published online by Cambridge University Press:  02 June 2010

Emmanuel Breuillard  and
Ben Green
Emmanuel Breuillard
Affiliation:
Laboratoire de Mathématiques Université Paris-Sud 11, 91405 Orsay cedex, France (emmanuel.breuillard@math.u-psud.fr)
Ben Green
Affiliation:
Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK (b.j.green@dpmms.cam.ac.uk)
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Abstract

We describe the structure of ‘K-approximate subgroups’ of torsion-free nilpotent groups, paying particular attention to Lie groups.

Three other works, by Fisher et al., by Sanders and by Tao, have appeared that independently address related issues. We comment briefly on some of the connections between these papers.

Keywords

approximate groupnilpotent progressionadditive combinatoricsFreiman's theorem

MSC classification

Secondary: 11B30: Arithmetic combinatorics; higher degree uniformity
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 10 , Issue 1 , January 2011 , pp. 37 - 57
Copyright
Copyright © Cambridge University Press 2010

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