Date of Award

5-1-2024

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Mathematics and Statistics

Dissertation/Thesis Chair

Anupam Srivastav

Committee Members

Marco Varisco, Boris Goldfarb, Changlong Zhong, Cristian Lenart

Subject Categories

Physical Sciences and Mathematics

Abstract

In this thesis we classify all finite groups where the corresponding truncated group ring over the ring of algebraic integers of quadratic imaginary fields has only trivial units. This is done by extending the thesis of Brian Rich to quadratic imaginary number fields and also covering the case of non-abelian groups over ordinary integers. We also show a different method to prove the theorems of Higman and Herman-Li for ordinary group rings. The motivation for determining the units of truncated group rings is in determining the subgroup of Swan classes that arises in integral representation theory.

Download

Share

COinS