Trivial units in group rings using Promislow's example of a torsion-free nonunique product group

William Carter

The purpose of this paper is to outline preliminary work in the investigation of nontrivial units in the group ring KG where K is a field and G is Promislow's simple example of a torsion-free non-unique product group. We will discuss the initial cases using right orderability and ultimately show that there are no invertible elements of support size 3.