The Margulis Zimmer Conjecture for Nonuniform Arithmetic Groups

Yehuda Shalom; Tyakal Venkataramana; George Willis

The Margulis Zimmer Conjecture for Nonuniform Arithmetic Groups

Group Theory 2026-07-19 v1

Authors: Yehuda Shalom , Tyakal Venkataramana , George Willis

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.

Cite

@article{arxiv.2607.17078,
  title  = {The Margulis Zimmer Conjecture for Nonuniform Arithmetic Groups},
  author = {Yehuda Shalom and Tyakal Venkataramana and George Willis},
  journal= {arXiv preprint arXiv:2607.17078},
  year   = {2026}
}

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17 pages