Interpretable groups are definable
  We prove that in an arbitrary o-minimal structure, every interpretable group is definably isomorphic to a definable one. We also prove that every definable group lives in a cartesian product of one-dimensional definable group-intervals (or one-dimensional definable groups). We discuss the general open question of elimination of imaginaries in an o-minimal structure. 
Janak Ramakrishnan, Ya'acov Peterzil, and Pantelis Eleftheriou
math.LO