Resesentations of finite groups and group rings

Abstract

Let G be a finite group and K be a field. The aim of this thesis is to study the representations of G over K and to observe the connections with group algebra KG. Fundamental problems in these areas include writing a complete set of irreducible K-representations of G, the character table of G and the explicit structure of KG that is closely related to the complete set of primitive central idempotents of KG. We address these problems and list complete answers for substantial classes of finite groups, with a special focus on metacyclic groups.