The Margulis Zimmer Conjecture for Nonuniform Arithmetic Groups

2026/07/19 by Yehuda Shalom, Tyakal Venkataramana, George Willis
#math.GR

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Abstract

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.

Related

• Arithmetic Groups and the Lehmer Conjecture
• Zimmer's conjecture for actions of SL(m,ℤ)
• Zimmer's conjecture for non-uniform lattices: escape of mass and growth of cocycles
• Subgroup growth of lattices in semisimple Lie groups
• Almost-minimal nonuniform lattices of higher rank