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 |
Keywords:
Zassenhaus conjecture; prime graphs; torsion units; partial augmentations; integral group rings; Kimmerle conjecture; normalized unit groups; Janko sporadic simple groupsReferences:
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