scholarly journals Torsion units in integral group rings of Janko simple groups

2010 ◽  
Vol 80 (273) ◽  
pp. 593-615 ◽  
Author(s):  
V. A. Bovdi ◽  
E. Jespers ◽  
A. B. Konovalov
Keyword(s):  
Simple Groups ◽  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings ◽  
Torsion Units

scholarly journals TORSION UNITS IN INTEGRAL GROUP RINGS OF CONWAY SIMPLE GROUPS

2011 ◽  
Vol 21 (04) ◽  
pp. 615-634 ◽  
Author(s):  
V. A. BOVDI ◽  
A. B. KONOVALOV ◽  
S. LINTON
Keyword(s):  
Unit Group ◽  
Simple Groups ◽  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings ◽  
Torsion Units

Using the Luthar–Passi method, we investigate the possible orders and partial augmentations of torsion units of the normalized unit group of integral group rings of Conway simple groups Co 1, Co 2 and Co 3.

scholarly journals On the Structure of Integral Group Rings of Sporadic Groups

2000 ◽  
Vol 3 ◽  
pp. 274-306 ◽  
Author(s):  
Frauke M. Bleher ◽  
Wolfgang Kimmerle
Keyword(s):  
Automorphism Groups ◽  
Symmetric Groups ◽  
Computational Procedure ◽  
Isomorphism Problem ◽  
Simple Groups ◽  
Group Rings ◽  
Integral Group ◽  
Sporadic Groups ◽  
Integral Group Rings ◽  
Sporadic Simple Groups

AbstractThe object of this article is to examine a conjecture of Zassenhaus and certain variations of it for integral group rings of sporadic groups. We prove the ℚ-variation and the Sylow variation for all sporadic groups and their automorphism groups. The Zassenhaus conjecture is established for eighteen of the sporadic simple groups, and for all automorphism groups of sporadic simple groups G which are different from G. The proofs are given with the aid of the GAP computer algebra program by applying a computational procedure to the ordinary and modular character tables of the groups. It is also shown that the isomorphism problem of integral group rings has a positive answer for certain almost simple groups, in particular for the double covers of the symmetric groups.

Coleman Automorphisms of Extensions of Finite Characteristically Simple Groups by Some Finite Groups

2021 ◽  
Vol 28 (04) ◽  
pp. 561-568
Author(s):  
Jinke Hai ◽  
Lele Zhao
Keyword(s):  
Abelian Group ◽  
Simple Group ◽  
Finite Groups ◽  
Finite Simple Group ◽  
Simple Groups ◽  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings ◽  
Inner Automorphism ◽  
Coleman Automorphism

Let [Formula: see text] be an extension of a finite characteristically simple group by an abelian group or a finite simple group. It is shown that every Coleman automorphism of [Formula: see text] is an inner automorphism. Interest in such automorphisms arises from the study of the normalizer problem for integral group rings.

scholarly journals Torsion units in integral group rings of metacyclic groups

1984 ◽  
Vol 19 (1) ◽  
pp. 103-114 ◽  
Author(s):  
César Polcino Milies ◽  
Sudarshan K. Sehgal
Keyword(s):  
Group Rings ◽  
Integral Group ◽  
Metacyclic Groups ◽  
Integral Group Rings ◽  
Torsion Units

scholarly journals On a conjecture of Zassenhaus on torsion units in integral group rings. II

1986 ◽  
Vol 97 (2) ◽  
pp. 201-201 ◽  
Author(s):  
C{ésar Polcino Milies ◽  
J{ürgen Ritter ◽  
Sudarshan K. Sehgal
Keyword(s):  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings ◽  
Torsion Units

scholarly journals Bass units as free factors in integral group rings of simple groups

2014 ◽  
Vol 404 ◽  
pp. 100-123 ◽  
Author(s):  
Jairo Z. Gonçalves ◽  
Robert M. Guralnick ◽  
Ángel del Río
Keyword(s):  
Simple Groups ◽  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings
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