Presentations for quaternionic $S$-unit groups
Number Theory
2015-09-08 v1 Group Theory
Geometric Topology
Rings and Algebras
Abstract
The purpose of this paper is to give presentations for projective -unit groups of the Hurwitz order in Hamilton's quaternions over the rational field . To our knowledge, this provides the first explicit presentations of an -arithmetic lattice in a semisimple Lie group with large. In particular, we give presentations for groups acting irreducibly and cocompactly on a product of Bruhat--Tits trees. We also include some discussion and experimentation related to the congruence subgroup problem, which is open when contains at least two odd primes. In the appendix, we provide code that allows the reader to compute presentations for an arbitrary finite set .
Cite
@article{arxiv.1404.6091,
title = {Presentations for quaternionic $S$-unit groups},
author = {Ted Chinburg and Holley Friedlander and Sean Howe and Michiel Kosters and Bhairav Singh and Matthew Stover and Ying Zhang and Paul Ziegler},
journal= {arXiv preprint arXiv:1404.6091},
year = {2015}
}