Hyperbolic unit groups
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- by S. O. Juriaans, I. B. S. Passi and Dipendra Prasad PDF
- Proc. Amer. Math. Soc. 133 (2005), 415-423 Request permission
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.References
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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
- MR Author ID: 136630
- Email: passi@mri.ernet.in
- Dipendra Prasad
- Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
- MR Author ID: 291342
- Email: dprasad@math.tifr.res.in
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 415-423
- MSC (2000): Primary 20C07, 16S34, 20F67
- DOI: https://doi.org/10.1090/S0002-9939-04-07578-1
- MathSciNet review: 2093062