Units in Group Rings of Free Products of Prime Cyclic Groups

Dokuchaev, Michael A. ; Singer, Maria Lucia Sobral

Canadian journal of mathematics, Tome 50 (1998) no. 2, pp. 312-322

Résumé

Let $G$ be a free product of cyclic groups of prime order. The structure of the unit group $U(\mathbb{Q}G)$ of the rational group ring $\mathbb{Q}G$ is given in terms of free products and amalgamated free products of groups. As an application, all finite subgroups of $U(\mathbb{Q}G)$ , up to conjugacy, are described and the Zassenhaus Conjecture for finite subgroups in $\mathbb{Z}G$ is proved. A strong version of the Tits Alternative for $U(\mathbb{Q}G)$ is obtained as a corollary of the structural result.

Détail

DOI : 10.4153/CJM-1998-016-2

Mots-clés : 20C07, 16S34, 16U60, 20E06, Free Products, Units in group rings, Zassenhaus Conjecture

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