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Cartan subgroups and regular points of o‐minimal groups

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Baro González, Elías and Berarducci, Alessandro and Otero, Margarita (2019) Cartan subgroups and regular points of o‐minimal groups. Journal of the London Mathematical Society . ISSN 1469-7750

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Official URL: https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/jlms.12216



Abstract

Let G be a group definable in an o-minimal structure M. We prove that the union of the Cartan subgroups of G is a dense subset of G. When M is an expansion of a real closed field we give a characterization of Cartan subgroups of G via their Lie algebras which allow us to prove firstly, that every Cartan subalgebra of the Lie algebra of G is the Lie algebra of a definable subgroup – a Cartan subgroup of G –, and secondly, that the set of regular points of G – a dense subset of G – is formed by points which belong to a unique Cartan subgroup of G.

Resumen (otros idiomas)

Item Type:Article
Uncontrolled Keywords:Lógica simbólica y matemática, Teoría de grupos
Palabras clave (otros idiomas):Mathematical logic and foundations, Group theory
Subjects:Sciences > Mathematics
Sciences > Mathematics > Group Theory
Sciences > Mathematics > Logic, Symbolic and mathematical
ID Code:57844
Deposited On:21 Nov 2019 11:30
Last Modified:21 Nov 2019 11:55

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