Research Projects

The study of dimension groups has been a significant area of research for a group G. Recently, the author has focused on the unit group of an integral group ring and its center. They have defined a filtration of the unit group of an integral group ring, which they call its dimension series. The extension of this concept to the unit group of an integral group ring leads to significant research. The author has also compiled two articles to describe the upper and lower central series of the unit group. While much is known about the upper central series, several fundamental questions remain unanswered for the lower central series. Understanding the residual nilpotence of this unit group, which is the triviality of the intersection of all members of its lower central series, is a significant problem in this direction. The author is interested in undertaking this study under a proposed project, with technical details enclosed. They have worked closely with Late Prof. I.B.S. Passi, who they collaborated on several articles on the unit group of an integral group ring. After his death, the author was approached to write articles, compile his collected works, and publish them in their Collected Works series. A consent for the publication has been received over email, and the author believes that working through the details of several of these articles will contribute to their understanding of the subject.