  This work can be thought as a contribution to the model theory of group
extensions. We study the groups G which are interpretable in the disjoint union
of two structures (seen as a two-sorted structure). We show that if one of the
two structures is superstable of finite Lascar rank and the Lascar rank is
definable, then G is an extension of a group internal to the (possibly)
unstable sort by a definable subgroup internal to the stable sort. In the final
part of the paper we show that if the unstable sort is an o-minimal expansion
of the reals, then G has a natural Lie structure and the extension is a
topological cover.
