Generators for Arithmetic Groups

TL;DR

This paper proves that non-cocompact irreducible lattices in higher rank semi-simple Lie groups have finite index subgroups generated by only three elements, revealing a new structural property of these groups.

Contribution

It establishes that such lattices contain finite index subgroups with a minimal generating set of three elements, a novel insight into their algebraic structure.

Findings

Existence of 3-generator subgroups of finite index

Structural simplification of non-cocompact lattices

Advancement in understanding generators of arithmetic groups

Abstract

We prove that any non-cocompact irreducible lattice in a higher rank semi-simple Lie group contains a subgroup of finite index, which has three generators.