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.
