RT Journal Article
T1 Cartan subgroups and regular points of o‐minimal groups
A1 Baro González, Elías
A1 Berarducci, Alessandro
A1 Otero, Margarita
AB 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.
PB London Mathematical Society
SN 1469-7750
YR 2019
FD 2019-10-01
LK https://hdl.handle.net/20.500.14352/13777
UL https://hdl.handle.net/20.500.14352/13777
LA eng
NO Ministerio de Ciencia e Innovación (España)
NO Ministerio de Economía y Competitividad (España)
NO Universidad Complutense de Madrid
NO MIUR
DS Docta Complutense
RD 9 abr 2025