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Torsion units in integral group rings of Janko simple groups. (English) Zbl 1209.16026

Summary: Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of integral group rings of Janko sporadic simple groups. As a consequence, we obtain that the Gruenberg-Kegel graph of the Janko groups \(J_1\), \(J_2\) and \(J_3\) is the same as that of the normalized unit group of their respective integral group ring.

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; MINION; LAGUNA
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References:

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