Zassenhaus Conjecture for Integral Group Rings of Simple Linear Groups

TL;DR

This paper proves the Zassenhaus conjecture holds for the integral group rings of the simple linear groups PSL(2,8) and PSL(2,17), advancing understanding of unit structures in these algebraic objects.

Contribution

It confirms the conjecture for specific simple linear groups, extending previous partial results and contributing to the broader effort to verify the conjecture.

Findings

Zassenhaus conjecture verified for PSL(2,8)

Zassenhaus conjecture verified for PSL(2,17)

Advances the classification of units in integral group rings

Abstract

We prove that the Zassenhaus conjecture is true for $PSL(2,8)$ and $PSL(2,17)$. This is a continuation of research initiated by W. Kimmerle, M. Hertweck and C. H\"ofert.