On the torsion units of the integral group ring of finite projective special linear groups

Abstract

H. J. Zassenhaus conjectured that any unit of finite order and augmentation one in the integral group ring of a finite group $G$ is conjugate in the rational group algebra to an element of $G$. One way to verify this is showing that such unit has the same distribution of partial augmentations as an element of $G$ and the HeLP Method provides a tool to do that in some cases. In this paper we use the HeLP Method to describe the partial augmentations of a hypothetical counterexample to the conjecture for the projective special linear groups.

14 pages. We fix an error of the previous version. The new proof is much shorter

References in corpus (3)

• Partial augmentations and Brauer character values of torsion units in group rings
• Zassenhaus Conjecture for Integral Group Rings of Simple Linear Groups
• Zassenhaus Conjecture on torsion units holds for $\mathrm{PSL}(2,p)$ with $p$ a Fermat or Mersenne prime

Cited by in corpus (3)

• On the Prime Graph Question for Integral Group Rings of 4-primary groups II
• Zassenhaus Conjecture on torsion units holds for $\mathrm{PSL}(2,p)$ with $p$ a Fermat or Mersenne prime
• On the first Zassenhaus conjecture and direct products