| Résume | Let G be a group. A subgroup H of G is a Cartan subgroup of
G if H is a maximal nilpotent subgroup of G, and for every normal finite
index subgroup X of H, X has finite index in its normalizer in G.
We consider Cartan subgroups of definably connect groups definable in
an o-minimal structure. In [BJ0] we proved that, in this context,
Cartan subgroups of G exist, they are definable and they fall in
finitely many conjugacy classes.
In this talk I will prove that the union of the Cartan subgroups is
dense 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 groups
definable in o-minimal structures, J. Inst. Math. Juissieu 13 no. 4
(2014) 849 - 893. |
