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Preprint Number 1249
1249. Elias Baro, Alessandro Berarducci, Margarita Otero Cartan subgroups and regular points of o-minimal groups E-mail: Submission date: 10 July 2017 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. Mathematics Subject Classification: 03C64, 20G15, 20E34 Keywords and phrases: Lie groups; algebraic groups; groups definable in o-minimal structures, Cartan subgroups |

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