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Search: MSC category 16U60 ( Units, groups of units )

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1. CJM 1998 (vol 50 pp. 312)

Dokuchaev, Michael A.; Singer, Maria Lucia Sobral
Units in group rings of free products of prime cyclic groups
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
Categories:20C07, 16S34, 16U60, 20E06

2. CJM 1998 (vol 50 pp. 401)

Li, Yuanlin
The hypercentre and the $n$-centre of the unit group of an integral group ring
In this paper, we first show that the central height of the unit group of the integral group ring of a periodic group is at most $2$. We then give a complete characterization of the $n$-centre of that unit group. The $n$-centre of the unit group is either the centre or the second centre (for $n \geq 2$).

Categories:16U60, 20C05

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