Integral group ring of the first Mathieu simple group

TL;DR

This paper examines the Zassenhaus conjecture for the unit group of the integral group ring of Mathieu group M11 and confirms related prime graph conjectures, advancing understanding of algebraic structures of sporadic simple groups.

Contribution

It provides the first verification of the Zassenhaus conjecture for M11 and confirms Kimmerle's prime graph conjecture for this group.

Findings

Confirmed Zassenhaus conjecture for M11

Validated Kimmerle's prime graph conjecture for M11

Enhanced understanding of unit groups in sporadic simple groups

Abstract

We investigated the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the simple Mathieu group M11. As a consequence, for this group we confirm the conjecture by Kimmerle about prime graphs.