Free products of groups and their group rings
by
Lukasz Wiechecki
Warsaw University

In the talk we will discuss some examples of computing U(R[G₁ * G₂]), the group of units in the group ring R[G₁ * G₂]). The techniques used in this case can be either of combinatorial or geometric nature. We will outline how applying the actions-of-groups-on-trees technique invented by Bass and Serre we can find presentation of U(k[C₂ * C₂]) for k a field of characteristics not equal to 2. We will also mention some results of Gerasimov and Bergman, and what follows from it for group rings.

Date received: August 8, 2000