Linear groups and group rings

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 of finite groups. We show, for example, that if G is nonabelian of order prime to 6, then contains two Bass cyclic units that generate a non-abelian free group.