Approximate subgroups
[Sous-groupes approximatifs]
Massicot, Jean-Cyrille1 ; Wagner, Frank O.2
1 tabacckludge ’Ecole normale supérieure de Rennes, Campus de Ker lann Avenue Robert Schuman, 35170 Bruz, France
2 Université Lyon 1, CNRS, Institut Camille Jordan UMR 5208 21 avenue Claude Bernard, 69622 Villeurbanne cedex, France
Journal de l’École polytechnique — Mathématiques, Tome 2 (2015), pp. 55-63.

Étant donné un sous-groupe approximatif A définissablement moyennable d’un groupe (local) dans une structure du premier ordre, il y a un sous-groupe H type-définissable normalisé par A et contenu dans A 4 tel que tout ensemble définissable contenant H est de mesure positive.

Given a definably amenable approximate subgroup A of a (local) group in some first-order structure, there is a type-definable subgroup H normalized by A and contained in A 4 such that every definable superset of H has positive measure.

DOI : 10.5802/jep.17
Classification : 11B30, 20N99, 03C98, 20A15
Keywords: Approximate subgroup, definability, definable amenability
Mot clés : Sous-groupe approximatif, moyennable, sous-groupe type-définissable
Massicot, Jean-Cyrille 1 ; Wagner, Frank O. 2

1 tabacckludge ’Ecole normale supérieure de Rennes, Campus de Ker lann Avenue Robert Schuman, 35170 Bruz, France
2 Université Lyon 1, CNRS, Institut Camille Jordan UMR 5208 21 avenue Claude Bernard, 69622 Villeurbanne cedex, France 
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Massicot, Jean-Cyrille; Wagner, Frank O. Approximate subgroups. Journal de l’École polytechnique — Mathématiques, Tome 2 (2015), pp. 55-63. doi : 10.5802/jep.17. http://archive.numdam.org/articles/10.5802/jep.17/

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