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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Hyperbolic unit groups


Authors: S. O. Juriaans, I. B. S. Passi and Dipendra Prasad
Journal: Proc. Amer. Math. Soc. 133 (2005), 415-423
MSC (2000): Primary 20C07, 16S34, 20F67
Published electronically: August 4, 2004
MathSciNet review: 2093062
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Abstract: In this paper we study the groups ${\mathcal{G}}$ whose integral group rings have hyperbolic unit groups ${\mathcal{U}(\mathbb{Z} {\mathcal{G}}) }$. We classify completely the torsion subgroups of $\mathcal{U}(\mathbb{Z} {\mathcal{G}})$ and the polycyclic-by-finite subgroups of the group ${\mathcal{G}}$. Finally, we classify the groups for which the boundary of ${\mathcal{U}(\mathbb{Z} {\mathcal{G}}) }$ has dimension zero.


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Additional Information

S. O. Juriaans
Affiliation: Instituto de Matemática e Estatística, CP. 666.281, CEP.05315-970, São Paulo, Brazil
Email: ostanley@ime.usp.br

I. B. S. Passi
Affiliation: Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211019, India
Email: passi@mri.ernet.in

Dipendra Prasad
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
Email: dprasad@math.tifr.res.in

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07578-1
PII: S 0002-9939(04)07578-1
Keywords: Hyperbolic group, group ring, unit group, Wedderburn decomposition.
Received by editor(s): March 20, 2003
Received by editor(s) in revised form: October 18, 2003
Published electronically: August 4, 2004
Additional Notes: This research was partially supported by CNPq-Brazil, FAPESP-Brazil.
Communicated by: Jonathan I. Hall
Article copyright: © Copyright 2004 American Mathematical Society