[Extensions du théorème de Schreiber sur les sous-groupes approximatifs discrets de ]
Dans cet article, nous donnons une autre démonstration du théorème de Schreiber : un sous-groupe approximatif discret infini de est relativement dense au voisinage d’un sous-espace. Nous déduisons aussi du théorème de Schreiber deux nouveaux résultats : le premier affirme qu’un sous-groupe approximatif discret infini de est la restriction d’un ensemble de Meyer à un épaississement d’un sous-espace linéaire de , et le second propose une extension du théorème de Schreiber au cas du groupe de Heisenberg.
In this paper we give an alternative proof of Schreiber’s theorem which says that an infinite discrete approximate subgroup in is relatively dense around a subspace. We also deduce from Schreiber’s theorem two new results. The first one says that any infinite discrete approximate subgroup in is a restriction of a Meyer set to a thickening of a linear subspace in , and the second one provides an extension of Schreiber’s theorem to the case of the Heisenberg group.
Accepté le :
Publié le :
DOI : 10.5802/jep.90
Keywords: Approximate groups, approximate lattices, Meyer sets
Mot clés : Groupes approximatifs, réseaux approximatifs, ensembles de Meyer
Alexander Fish 1
CC-BY 4.0
@article{JEP_2019__6__149_0,
author = {Alexander Fish},
title = {Extensions of {Schreiber{\textquoteright}s} theorem on discrete approximate subgroups in~$\protect \mathbb{R}^d$},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {149--162},
publisher = {\'Ecole polytechnique},
volume = {6},
year = {2019},
doi = {10.5802/jep.90},
mrnumber = {3915195},
zbl = {07033368},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.90/}
}
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JO - Journal de l’École polytechnique — Mathématiques
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PB - École polytechnique
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Alexander Fish. Extensions of Schreiber’s theorem on discrete approximate subgroups in $\protect \mathbb{R}^d$. Journal de l’École polytechnique — Mathématiques, Tome 6 (2019), pp. 149-162. doi : 10.5802/jep.90. https://jep.centre-mersenne.org/articles/10.5802/jep.90/
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