Definable groups as homomorphic images of semilinear and field-definable   groups
  We analyze definably compact groups in o-minimal expansions of ordered groups as a combination of semi-linear groups and groups definable in o-minimal expansions of real closed fields. The analysis involves structure theorems about their locally definable covers. As a corollary, we prove the Compact Domination Conjecture in o-minimal expansions of ordered groups. 
Pantelis Eleftheriou and Ya'acov Peterzil
math.LO