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arXiv · 0905.4295

The Unit Group of Small Group Algebras and the Minimum Counterexample to the Isomorphism Problem

Leo Creedon
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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.

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Leo Creedon. 2009-05-26. The Unit Group of Small Group Algebras and the Minimum Counterexample to the Isomorphism Problem. https://arxiv.org/abs/0905.4295

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