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Units in Group Rings of Free Products of Prime Cyclic Groups
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- Journal:
- Canadian Journal of Mathematics / Volume 50 / Issue 2 / 01 April 1998
- Published online by Cambridge University Press:
- 20 November 2018, pp. 312-322
- Print publication:
- 01 April 1998
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- Article
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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.
