Hyperbolic unit groups

Juriaans, S.; Passi, I.; Prasad, Dipendra

doi:10.1090/S0002-9939-04-07578-1

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.

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