Integral group ring of the Suzuki sporadic simple group

TL;DR

This paper investigates the Zassenhaus conjecture for the Suzuki sporadic simple group's integral group ring using the Luthar--Passi method, confirming related conjectures about prime graphs.

Contribution

It applies the Luthar--Passi method to a complex sporadic simple group, providing new evidence for the Zassenhaus and Kimmerle's conjectures.

Findings

Confirmed the Zassenhaus conjecture for Suz

Validated Kimmerle's conjecture on prime graphs for Suz

Enhanced understanding of units in integral group rings of sporadic groups

Abstract

Using the Luthar--Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the Suzuki sporadic simple group Suz. As a consequence, for this group we confirm the Kimmerle's conjecture on prime graphs.