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Torsion units in integral group rings of Janko simple groups


Authors: V. A. Bovdi, E. Jespers and A. B. Konovalov
Journal: Math. Comp. 80 (2011), 593-615
MSC (2010): Primary 16S34, 20C05; Secondary 20D08
DOI: https://doi.org/10.1090/S0025-5718-2010-02376-2
Published electronically: June 9, 2010
MathSciNet review: 2728996
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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.


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Additional Information

V. A. Bovdi
Affiliation: Institute of Mathematics, University of Debrecen, P.O. Box 12, H-4010 Debrecen, Hungary
Email: vbovdi@math.unideb.hu

E. Jespers
Affiliation: Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussel, Belgium
Email: efjesper@vub.ac.be

A. B. Konovalov
Affiliation: School of Computer Science, University of St Andrews, Jack Cole Building, North Haugh, St Andrews, Fife, KY16 9SX, Scotland
Email: alexk@mcs.st-andrews.ac.uk

DOI: https://doi.org/10.1090/S0025-5718-2010-02376-2
Keywords: Zassenhaus conjecture, prime graph, torsion unit, partial augmentation, integral group ring
Received by editor(s): April 27, 2007
Received by editor(s) in revised form: September 7, 2009
Published electronically: June 9, 2010
Additional Notes: The research was supported by OTKA No. K68383, Onderzoeksraad of Vrije Universiteit Brussel, Fonds voor Wetenschappelijk Onderzoek (Belgium), Flemish-Polish bilateral agreement BIL2005/VUB/2006, Francqui Stichting (Belgium) grant ADSI107 and The Royal Society of Edinburgh International Exchange Programme
Dedicated: Dedicated to the memory of Professor I. S. Luthar
Article copyright: © Copyright 2010 American Mathematical Society