Mini-Workshop: Arithmetik von Gruppenringen

Abstract

The theory of group rings has many connections to other mathematical areas, such as number theory, K-theory, topology, representation theory, homological algebra and of course the theory of finite and infinite groups, and ring theory. This mini workshop focussed on the arithmetics of integral group rings, particularly their multiplicative structure and unit groups. The central topics were the recent developments in connection with the first Zassenhaus conjecture, constructive descriptions of units and subgroups of units, cohomological and representation theoretical methods, a complete description of the units of integral group rings of some classes of finite groups, and interactions with semigroup rings and orders.