Hyperbolicity of Orders of Quaternions Algebras and Group Rings
Rings and Algebras
2007-05-23 v2 Group Theory
Abstract
For a given divison algebra of the quaternions we construct two types of units: Pell units and Gauss units. If K is a rational quadratic extension and G is a finite group, we classify R and G, s.t., the unit group U(RG) of augmentation one is hyperbolic. In particular we give necessary and sufficient conditions when G is the quaternion group of order 8. In this case, the hyperbolic boundary is isomorphic to the 2-dimensional sphere. As a result we reach a class of groups of one end, that are not virtually free.
Keywords
Cite
@article{arxiv.math/0610699,
title = {Hyperbolicity of Orders of Quaternions Algebras and Group Rings},
author = {S. O. Juriaans A. C. Souza Filho},
journal= {arXiv preprint arXiv:math/0610699},
year = {2007}
}
Comments
This report is part of the first chapter of the second author's PhD. Thesis. It was included a result in main theorem and a sketch of its proof before it, as well as two new references