#### Date of Award

6-1998

#### Degree Name

Doctor of Philosophy

#### Department

Mathematics

#### First Advisor

Dr. Joseph Buckley

#### Second Advisor

Dr. John Martino

#### Third Advisor

Dr. Thomas Richardson

#### Fourth Advisor

Dr. Kung Wei Yang

#### Abstract

Given a finite group* G* and the ring of integers, one can form the integral group ring *ZG* . A natural problem to investigate is to find a description of the group of units for this ring *ZG.* Since the unit problem for integral group rings arises in the contexts of algebraic topology, number theory, and algebra, it is an important question to try to answer. For this reason, it has drawn the attention of researchers from diverse areas of mathematics.

Graham Higman (circa 1940) made substantial contributions to the solution of this problem, in the case where *G* was a finite abelian group. From then on. the main focus of the research in this area has been in the case where *G* was a finite non-abelian group. Although there are some results for *U(ZG)* for various groups *G*, very little is known with respect to explicit descriptions of *U(ZG )*.

In this dissertation, we address the following question: If we have a description of *U(ZG)*, what information can we obtain about *U(ZG*)*, where *G' = G x Cp* and *p* is prime? A general algebraic framework using short-exact sequences is developed to study this problem. In addition, known and new results are obtained in the case where *p* = 2.

#### Access Setting

Dissertation-Open Access

#### Recommended Citation

Low, Richard M., "Units in Integral Group Rings for Direct Products" (1998). *Dissertations*. 1550.

https://scholarworks.wmich.edu/dissertations/1550

## Comments

Fifth Advisor: Dr. Michael Parmenter