Approximate subgroups
Journal de l’École polytechnique - Mathématiques, Volume 2  (2015), p. 55-63

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.

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.

DOI : https://doi.org/10.5802/jep.17
Classification:  11B30,  20N99,  03C98,  20A15
Keywords: Approximate subgroup, definability, definable amenability
@article{JEP_2015__2__55_0,
     author = {Massicot, Jean-Cyrille and Wagner, Frank O.},
     title = {Approximate subgroups},
     journal = {Journal de l'\'Ecole polytechnique - Math\'ematiques},
     publisher = {Ecole polytechnique},
     volume = {2},
     year = {2015},
     pages = {55-63},
     doi = {10.5802/jep.17},
     language = {en},
     url = {http://www.numdam.org/item/JEP_2015__2__55_0}
}
Massicot, Jean-Cyrille; Wagner, Frank O. Approximate subgroups. Journal de l’École polytechnique - Mathématiques, Volume 2 (2015) , pp. 55-63. doi : 10.5802/jep.17. http://www.numdam.org/item/JEP_2015__2__55_0/

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