IJPAM: Volume 49, No. 4 (2008)

THE UNIT GROUP OF SMALL GROUP ALGEBRAS AND
THE MINIMUM COUNTEREXAMPLE TO
THE ISOMORPHISM PROBLEM

Leo Creedon
Institute of Technology Sligo
Sligo, IRELAND
e-mail: creedon.leo@itsligo.ie


Abstract.Let $KG$ denote the group algebra of the group $G$ over the field $K$ and let $U(KG)$ denote its group of units. Here without the use of a computer we give presentations for the unit groups of all group algebras $KG$, where the size of $KG$ is less than $1024$. As a consequence we find the minimum counterexample to the Isomorphism Problem for group algebras.

Received: August 14, 2008

AMS Subject Classification: 16S34, 16U60, 20C05

Key Words and Phrases: group ring, group algebra, unit group, isomorphism problem

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 49
Issue: 4