Published online by Cambridge University Press: 17 April 2009
Recent developments on the isomorphism and other group ring problems are amply reviewed in Sehgal's book, Topics in group rings. The aim of this expository paper is to complement the content of Sehgal's book. Our main emphasis is the presentation of some results due to Saksonov which are published in Russian and do not seem well-known to the English reader. We also draw the reader's attention to some unpublished results of Higman.