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Torsion units in integral group ring of the Mathieu simple group \(M_{22}\). (English) Zbl 1225.16017

Summary: We investigate the possible character values of torsion units of the normalized unit group of the integral group ring of the Mathieu sporadic group \(M_{22}\). We confirm the Kimmerle conjecture on prime graphs for this group and specify the partial augmentations for possible counterexamples to the stronger Zassenhaus conjecture.

MSC:

16U60 Units, groups of units (associative rings and algebras)
20C05 Group rings of finite groups and their modules (group-theoretic aspects)
16S34 Group rings
20D08 Simple groups: sporadic groups

Software:

GAP; LAGUNA
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References:

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