Bicyclic units, Bass cyclic units and free groups

Details Bicyclic units, Bass cyclic units and free groups Bicyclic units, Bass cyclic units and free groups

2006-12-04

arxiv.org/abs/math/0612091v2

Mathematics

Rings and Algebras

15 pages

Scientific paper

Let $G$ be a finite group and $\Z G$ its integral group ring. We show that if $\alpha$ is a non-trivial bicyclic unit of $\Z G$, then there are bicyclic units $\beta$ and $\gamma$ of different types, such that $\GEN{\alpha,\beta}$ and $\GEN{\alpha,\gamma}$ are non-abelian free groups. In case that $G$ is non-abelian of order coprime with 6, then we prove the existence of a bicyclic unit $u$ and a Bass cyclic unit $v$ in $\Z G$, such that for every positive integer $m$ big enough, $\GEN{u^m,v}$ is a free non-abelian group.

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