Cartan subgroups of groups definable in o-minimal structures

2011/09/20 by Elias Baro, Elías Baro, Eric Jaligot +5
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR

paper · pdf · doi:10.48550/arxiv.1109.4349

Some details have been added in the proof of Theorem 57, via Remark 36

openalex publication_date 2011/09/20 · arxiv created 2012/11/20 · arxiv updated 2012/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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, in general very largely in terms of the dimension.

Related

• Groups definable in o-minimal structures: various properties and a diagram
• Commutators in groups definable in o-minimal structures
• Solvable groups definable in o-minimal structures
• Characterizing o-minimal groups in tame expansions of o-minimal\n structures
• Definable rank, o-minimal groups, and Wiegold's problem