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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
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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 Free Products, Units in group rings, Zassenhaus Conjecture
MSC Classifications: 20C07, 16S34, 16U60, 20E06 show english descriptions Group rings of infinite groups and their modules [See also 16S34]
Group rings [See also 20C05, 20C07], Laurent polynomial rings
Units, groups of units
Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
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
 

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