MOSTOW - MARGULIS RIGIDITY WITH LOCALLY COMPACT TARGETS 3 Construction

Let ? be a lattice in a simple higher rank Lie group G. We describe all locally compact (not necessarily Lie) groups H in which ? can be embedded as a lattice. For lattices ? in rank one groups G (with the only exception of non-uniform lattices in G ' SL 2 (R), which are virtually free groups) we give a similar description of all possible locally compact groups H, in which ? can be embedded as a uniform lattice. 1. Introduction and Statement of the Main Results Throughout this paper we use the following terminology: (semi)simple Lie group stands for (semi)simple, connected real Lie group with nite center and no non-trivial compact factors. If (semi)simple Lie groups G, G 0 are locally isomorphic we write