scholarly journals Torsion units in the integral group ring of PSL(3, 4)

2015 ◽  
Vol 15 (01) ◽  
pp. 1650013
Author(s):  
Joe Gildea ◽  
Alexander Tylyshchak
Keyword(s):  
Simple Group ◽  
Group Ring ◽  
Integral Group Ring ◽  
Integral Group ◽  
Zassenhaus Conjecture ◽  
Torsion Units

We investigate the Zassenhaus Conjecture for the integral group ring of the simple group PSL(3, 4).

scholarly journals Torsion Units in Integral Group Ring of the Mathieu Simple Group M22

2008 ◽  
Vol 11 ◽  
pp. 28-39 ◽  
Author(s):  
V. A. Bovdi ◽  
A. B. Konovalov ◽  
S. Linton
Keyword(s):  
Simple Group ◽  
Group Ring ◽  
Unit Group ◽  
Integral Group Ring ◽  
Integral Group ◽  
Sporadic Group ◽  
Prime Graphs ◽  
Zassenhaus Conjecture ◽  
Torsion Units

AbstractWe investigate the possible character values of torsion units of the normalized unit group of the integral group ring of the Mathieu sporadic group M22. We confirm the Kimmerle conjecture on prime graphs for this group and specify the partial augmentations for possible counterexamples to the stronger Zassenhaus conjecture.

scholarly journals Torsion units in integral group ring of Higman-Sims simple group

2010 ◽  
Vol 47 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Victor Bovdi ◽  
Alexander Konovalov
Keyword(s):  
Simple Group ◽  
Group Ring ◽  
Unit Group ◽  
Integral Group Ring ◽  
Integral Group ◽  
Sporadic Group ◽  
Prime Graphs ◽  
Zassenhaus Conjecture ◽  
Torsion Units

Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the Higman-Sims simple sporadic group HS. As a consequence, we confirm Kimmerle’s conjecture on prime graphs for this sporadic group.

scholarly journals INTEGRAL GROUP RING OF THE MATHIEU SIMPLE GROUP M24

2012 ◽  
Vol 11 (01) ◽  
pp. 1250016 ◽  
Author(s):  
VICTOR BOVDI ◽  
ALEXANDER KONOVALOV
Keyword(s):  
Simple Group ◽  
Group Ring ◽  
Unit Group ◽  
Positive Answer ◽  
Integral Group Ring ◽  
Integral Group ◽  
Sporadic Group ◽  
Prime Graphs ◽  
Zassenhaus Conjecture

We study the Zassenhaus conjecture for the normalized unit group of the integral group ring of the Mathieu sporadic group M24. As a consequence, for this group we give a positive answer to the question by Kimmerle about prime graphs.

scholarly journals Integral group ring of Rudvalis simple group

2009 ◽  
Vol 61 (1) ◽  
pp. 1-13 ◽  
Author(s):  
V. A. Bovdi ◽  
A. B. Konovalov
Keyword(s):  
Simple Group ◽  
Group Ring ◽  
Integral Group Ring ◽  
Integral Group

scholarly journals ZASSENHAUS CONJECTURE FOR INTEGRAL GROUP RING OF SIMPLE LINEAR GROUPS

2013 ◽  
Vol 12 (06) ◽  
pp. 1350016 ◽  
Author(s):  
JOE GILDEA
Keyword(s):  
Group Ring ◽  
Integral Group Ring ◽  
Linear Groups ◽  
Integral Group ◽  
Zassenhaus Conjecture

We prove that the Zassenhaus conjecture is true for PSL(2,8) and PSL(2,17). This is a continuation of research initiated by Kimmerle, Hertweck and Höfert.

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