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Cartan subgroups of groups definable in o-minimal structures

Part of: Topological and differentiable algebraic systems Model theory

Published online by Cambridge University Press:  28 November 2013

Elías Baro ,
Eric Jaligot  and
Margarita Otero
Elías Baro
Affiliation:
Departamento de Álgebra, Facultad de Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
Eric Jaligot
Affiliation:
Institut Fourier, CNRS, Université Grenoble I, 100 rue des maths, BP 74, 38402 St Martin d’Hères cedex, France
Margarita Otero
Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain ([email protected])
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Abstract

We prove that groups definable in o-minimal structures have Cartan subgroups, and only finitely many conjugacy classes of such subgroups. We also delineate with precision how these subgroups cover the ambient group.

Keywords

Lie groupssemialgebraic groupsgroups definable in o-minimal structuresCartan subgroups

MSC classification

Secondary: 22A05: Structure of general topological groups 03C64: Model theory of ordered structures; o-minimality
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 13 , Issue 4 , October 2014 , pp. 849 - 893
Copyright
©Cambridge University Press 2013 

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