scholarly journals Integral group ring of the first Mathieu simple group

2010 ◽  
pp. 237-245 ◽  
Author(s):  
Victor Bovdi ◽  
Alexander Konovalov
Keyword(s):  
Simple Group ◽  
Group Ring ◽  
Integral Group Ring ◽  
Integral 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 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 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 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 On the prime graph question for almost simple groups with an alternating socle

2017 ◽  
Vol 27 (03) ◽  
pp. 333-347 ◽  
Author(s):  
Andreas Bächle ◽  
Mauricio Caicedo
Keyword(s):  
Simple Group ◽  
Group Ring ◽  
Prime Graph ◽  
Integral Group Ring ◽  
Simple Groups ◽  
Alternating Group ◽  
Integral Group ◽  
Almost Simple Group ◽  
Almost Simple Groups

Let [Formula: see text] be an almost simple group with socle [Formula: see text], the alternating group of degree [Formula: see text]. We prove that there is a unit of order [Formula: see text] in the integral group ring of [Formula: see text] if and only if there is an element of that order in [Formula: see text] provided [Formula: see text] and [Formula: see text] are primes greater than [Formula: see text]. We combine this with some explicit computations to verify the prime graph question for all almost simple groups with socle [Formula: see text] if [Formula: see text].

On Automorphisms of Complete Algebras And The Isomorphism Problem for Modular Group Rings

1990 ◽  
Vol 42 (3) ◽  
pp. 383-394 ◽  
Author(s):  
Frank Röhl
Keyword(s):  
Group Ring ◽  
Modular Group ◽  
Isomorphism Problem ◽  
Nilpotency Class ◽  
Affirmative Answer ◽  
Integral Group Ring ◽  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings ◽  
Analogous Question

In [5], Roggenkamp and Scott gave an affirmative answer to the isomorphism problem for integral group rings of finite p-groups G and H, i.e. to the question whether ZG ⥲ ZH implies G ⥲ H (in this case, G is said to be characterized by its integral group ring). Progress on the analogous question with Z replaced by the field Fp of p elements has been very little during the last couple of years; and the most far reaching result in this area in a certain sense - due to Passi and Sehgal, see [8] - may be compared to the integral case, where the group G is of nilpotency class 2.

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