Elsevier

Journal of Algebra

Volume 295, Issue 1, 1 January 2006, Pages 94-118
Journal of Algebra

Linear groups and group rings

https://doi.org/10.1016/j.jalgebra.2005.02.009Get rights and content
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Abstract

This paper consists of two parts. The first is concerned with free products in linear groups and uses the usual “ping pong” lemma and attractors to prove the results. What is new here is that we allow certain subspaces of V associated with the semisimple and generalized transvection operators to have dimensions larger than 1. The second part is concerned with applications of this machinery to integral groups rings Z[G] of finite groups. We show, for example, that if G is nonabelian of order prime to 6, then Z[G] contains two Bass cyclic units that generate a non-abelian free group.

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1

The author's research was supported in part by CNPq grant 303.756/82-5 and Fapesp-Brasil, Proj. Tematico 00/07.291-0.

2

The author's research was supported in part by NSA grant 144-LQ65.