Hyperbolic Unit Groups and Quaternion Algebras
Rings and Algebras
2009-01-14 v3 Group Theory
Abstract
We Classify the rational quadratic extensions K and the finite groups G for which the group ring R[G] of G over the ring R of integers of K has the property that the group of units of augmentation 1 of R[G] is hyperbolic. We also construct units in a non-split quaternion algebra over R.
Cite
@article{arxiv.0709.2161,
title = {Hyperbolic Unit Groups and Quaternion Algebras},
author = {S. O. Juriaans and I. B. S. Passi and A. C. Souza Filho},
journal= {arXiv preprint arXiv:0709.2161},
year = {2009}
}
Comments
15 pages, this work is part of the PHd. Thesis of the third author. The paper was accepted in Proceedings Mathematical Sciences