Discrete groups without finite quotients

TL;DR

This paper constructs an infinite discrete subgroup of the hyperbolic 3-space isometry group that has no nontrivial finite quotients, providing a novel example in geometric group theory.

Contribution

It introduces a new example of a discrete group with trivial finite quotients, expanding understanding of group structures in hyperbolic geometry.

Findings

Constructed an infinite discrete subgroup with no nontrivial finite quotients

Demonstrated existence of such groups in hyperbolic 3-space

Contributed to the classification of discrete groups in geometric topology

Abstract

We construct an infinite discrete subgroup of the isometry group of $\mathbb H^3$ with no finite quotients other than the trivial group.