Cartan subgroups of groups definable in o-minimal structures

Abstract

We prove that groups definable in o-minimal structures have Cartan subgroups, and only finitely many conjugacy classes of such subgroups. We also delineate with precision how these subgroups cover the ambient group, in general very largely in terms of the dimension.

Some details have been added in the proof of Theorem 57, via Remark 36