Dr. Joe Gildea

Project Title:           Units of group Algebras

Supervisor:                Dr. Joe Gildea

Funding Body:   IT Sligo President’s Bursary Awards

Description of the project

Let KG be the group algebra of the group G over the field K. An element

of KG is invertible, if there exists an element of KG, which we shall denote

by a-1 in KG, called it’s inverse, such that a.a-1 = a-1.a = 1. The set of

invertible elements of KG form a group called the unit group of KG, denoted

by U(KG).

This project aims to investigate the structure of U(FpkG) for certain

groups up to order 64, where Fpk is the Galois field of pk-elements.

Currently, there exists techniques to find the structure of U(FpkG). We aim

to extend these techniques, construct new techniques and combine new and

old techniques to find the structure of U(FpkG) for certain groups up to order

64.