Hypercentral unit groups and the hyperbolicity of a modular group algebra

2006/10/26 by Iwaki, E., Juriaans, S. O.
#16S34 #16U60 #20C07 #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.math/0610803

Abstract

We classify groups G such that the unit group U(ZG) is hypercentral. In the second part we classify groups G whose modular group algebra has hyperbolic unit group V(KG).

Related

• Group rings whose group of units is hyperbolic
• Hyperbolic Unit Groups and Quaternion Algebras
• Jordan decomposition and hypercentral units in integral group rings
• Hyperbolicity of Orders of Quaternions Algebras and Group Rings
• Modular group algebras whose group of unitary units is locally nilpotent