On the existence of irreducible lattices (Q1057372)

Let G be a noncompact connected linear semisimple Lie group. A lattice in G is a discrete subgroup \(\Gamma\) with G/\(\Gamma\) of finite volume. If G has no compact factors, has a proper connected normal subgroup, and G/\(\Gamma\) is noncompact, Margulis and Ragunathan have given a necessary condition for \(\Gamma\) to be irreducible in G. The author sharpens this necessary condition to the condition that G must be \({\mathbb{Q}}\)-simple modulo compact factor and proves a converse under an extra hypothesis. This criterion is used to construct examples of irreducible lattices.