Definably simple groups in O-minimal structures

Let G = [G;.] be a group definable in an o-minimal structure M. A subset H of G is G-definable if H is definable in the structure [G; .] (while defina ble means definable in the structure M). Assume G has no G definable proper subgroup of finite index. In this paper we prove that if G has no nontrivi al abelian normal subgroup, then G is the direct product of G-definable sub groups H-1,...,H-k such that each H-i is definably isomorphic to a semialge braic linear group over a definable real closed field. As a corollary we ob tain an o-minimal analogue of Cherlin's conjecture.