location:  Publications → journals → CJM
Abstract view

# Units in group rings of free products of prime cyclic groups

Published:1998-04-01
Printed: Apr 1998
• Michael A. Dokuchaev
• Maria Lucia Sobral Singer
 Format: HTML LaTeX MathJax PDF PostScript

## Abstract

Let $G$ be a free product of cyclic groups of prime order. The structure of the unit group ${\cal U}(\Q G)$ of the rational group ring $\Q G$ is given in terms of free products and amalgamated free products of groups. As an application, all finite subgroups of ${\cal U}(\Q G)$, up to conjugacy, are described and the Zassenhaus Conjecture for finite subgroups in $\Z G$ is proved. A strong version of the Tits Alternative for ${\cal U}(\Q G)$ is obtained as a corollary of the structural result.
 Keywords: Free Products, Units in group rings, Zassenhaus Conjecture
 MSC Classifications: 20C07 - Group rings of infinite groups and their modules [See also 16S34] 16S34 - Group rings [See also 20C05, 20C07], Laurent polynomial rings 16U60 - Units, groups of units 20E06 - Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations

 top of page | contact us | privacy | site map |