%0 Journal Article
%A Baro González, Elías
%A Berarducci, Alessandro
%A Otero, Margarita
%T Cartan subgroups and regular points of o‐minimal groups
%D 2019
%@ 1469-7750
%U https://hdl.handle.net/20.500.14352/13777
%X 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.
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