Torsion units in integral group ring of Higman-Sims simple group

TL;DR

This paper investigates the structure of units in the integral group ring of the Higman-Sims group, confirming conjectures about their properties and prime graphs using the Luthar-Passi method.

Contribution

It applies the Luthar-Passi method to verify the Zassenhaus and Kimmerle's conjectures for the Higman-Sims group, a sporadic simple group.

Findings

Confirmed the Zassenhaus conjecture for HS units

Verified Kimmerle's conjecture on prime graphs for HS

Enhanced understanding of units in sporadic group rings

Abstract

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