Proceedings of the American Mathematical Society

Author(s): S. O. Juriaans; I. B. S. Passi; Dipendra Prasad
Journal: Proc. Amer. Math. Soc. 133 (2005), 415-423.
MSC (2000): Primary 20C07, 16S34, 20F67
Posted: August 4, 2004
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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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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

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