Hyperbolic unit groups and quaternion algebras

Juriaans, S. O. ; Passi, I. B. S. ; Filho, A. C. Souza (2009) Hyperbolic unit groups and quaternion algebras Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 119 (1). pp. 9-22. ISSN 0253-4142

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Official URL: http://www.ias.ac.in/mathsci/vol119/feb2009/PM0020...

Related URL: http://dx.doi.org/10.1007/s12044-009-0002-7

Abstract

We classify the quadratic extensions K = Q[√ d] and the finite groups G for which the group ring oK[G] of G over the ring oK of integers of K has the property that the group U1 (oK[G]) of units of augmentation 1 is hyperbolic. We also construct units in the Z-order H(oK) of the quaternion algebra H(K) = (-1,-1/K) , when it is a division algebra.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Hyperbolic Groups; Quaternion Algebras; Free Groups; Group Rings; Units
ID Code:87298
Deposited On:17 Mar 2012 12:39
Last Modified:19 May 2016 02:41

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