Hypercentral unit groups and the hyperbolicity of a modular group algebra. (English) Zbl 1142.16300
Summary: We classify groups \(G\) such that the unit group \(\mathcal U_1(\mathbb{Z} G)\) is hypercentral. In the second part, we classify groups \(G\) whose modular group algebra has hyperbolic unit groups \(\mathcal U_1(KG)\).
For details of this announcement see the authors’ paper [Commun. Algebra 36, No. 4, 1336-1345 (2008; Zbl 1149.16028)].
For details of this announcement see the authors’ paper [Commun. Algebra 36, No. 4, 1336-1345 (2008; Zbl 1149.16028)].
MSC:
| 16U60 | Units, groups of units (associative rings and algebras) |
| 20C07 | Group rings of infinite groups and their modules (group-theoretic aspects) |
| 16S34 | Group rings |
