Torsion units in integral group rings of Janko simple groups

2006/08/17 by V. A. Bovdi, Bovdi, V. A., E. Jespers +3
Mathematics · #16S34 #20C05 #20D08 #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA) #math.GR #math.RA #msc:16S34 #msc:20C05 #msc:20D08

paper · pdf · doi:10.48550/arxiv.math/0608441

23 pages, to appear in Math.Comp.

arxiv created 2010/05/05 · arxiv updated 2010/05/06

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 J₁, J₂ and J₃ is the same as that of the normalized unit group of their respective integral group ring.

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