  An argument of A.Borel shows that every compact connected Lie group is
homeomorphic to the Cartesian product of its derived subgroup and a torus. We
prove a parallel result for definably compact definably connected groups
definable in an o-minimal expansion of a real closed field. As opposed to the
Lie case, however, we provide an example showing that the derived subgroup may
not have a definable semidirect complement.
