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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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