In Goldman's book on Complex Hyperbolic Geometry, on page 203, it is stated that for a real semisimple Lie group $G$, the following are equivalent:
$G$ contains a nonempty open subset of elliptic elements (which are elements of maximal compact subgroups of $G$, i.e. fixing a point in the associated symmetric space), and
$G$ admits a compact Cartan subgroup.
Does anyone know how to prove the implication $1\Rightarrow 2$ ?
