ALGB seminar: Wei-Liang Sun (National Taiwan Normal University)

Title: The multiplicative Jordan decomposition in integral group rings

Abstract:
In this talk, I will present the development of the multiplicative Jordan decomposition (MJD) problem in integral group rings. This problem was proposed by Alfred W. Hales and Inder Bir S. Passi in 1991. The purpose is to classify finite groups such that every unit in their integral group ring can be decomposed into a product of a semisimple unit and a unipotent unit. This classification has not been completed. I will also present our results and questions for the groups Q_8xC_p where Q_8 is the quaternion group of order 8 and C_p is the cyclic group of a prime order p with a certain condition.