The Margulis Zimmer Conjecture for Nonuniform Arithmetic Groups

We prove that every infinite subgroup of a higher rank irreducible lattice in a semi-simple Lie group has finite index in the lattice, proving the Margulis-Zimmer conjecture for these lattices.

The method of proof combines the method used in a work of Shalom and Willis and also some work of Raghunathan and Venkataramana.