2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/231440Let $KG$ 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.6 pagesRings and AlgebrasGroup Theory16S34; 16U60; 20C05text