Torsion units in integral group rings of Janko simple groups

Abstract

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.

23 pages, to appear in Math.Comp.

References in corpus (1)

• Partial augmentations and Brauer character values of torsion units in group rings

Cited by in corpus (7)

• Integral group ring of the McLaughlin simple group
• Torsion units in integral group ring of the Mathieu simple group M22
• Integral group ring of the Mathieu simple group M23
• Kimmerle conjecture for the Held and O'Nan sporadic simple groups
• Integral group ring of the Mathieu simple group M24
• Integral group ring of Rudvalis simple group
• Integral group ring of the Mathieu simple group M12