Let G be a group. A subgroup H of G is a Cartan subgroup ofG if H is a maximal nilpotent subgroup of G, and for every normal finiteindex subgroup X of H, X has finite index in its normalizer in G.
We consider Cartan subgroups of definably connect groups definable inan o-minimal structure. In [BJ0] we proved that, in this context,Cartan subgroups of G exist, they are definable and they fall infinitely many conjugacy classes.
In this talk I will prove that the union of the Cartan subgroups isdense in the group, which was the main question left open in [BBO].
(Joint work with Elías Baro and Alessandro Berarducci.)
[BJ0] E.Baro, E. Jaligot and M.Otero. Cartan subgroups of groupsdefinable in o-minimal structures, J. Inst. Math. Juissieu 13 no. 4(2014) 849 – 893.