Conjugacy classes of torsion units of the integral group ring of dp

1983 ◽  
Vol 11 (14) ◽  
pp. 1607-1627 ◽  
Author(s):  
Ashwani K. Bhandari ◽  
Indar S. Luthar
Keyword(s):  
Group Ring ◽  
Conjugacy Classes ◽  
Integral Group Ring ◽  
Integral Group ◽  
Torsion Units

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 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).

On the Conjugacy Classes in an Integral Group Ring

1978 ◽  
Vol 21 (4) ◽  
pp. 491-496 ◽  
Author(s):  
Alan Williamson
Keyword(s):  
Finite Order ◽  
Direct Product ◽  
Group Ring ◽  
Periodic Group ◽  
Conjugacy Classes ◽  
Integral Group Ring ◽  
Integral Group ◽  
Quaternion Group

Let G be a periodic group and ZG its integral group ring. The elements ±g(g∈G) are called the trivial units of ZG. In [1], S. D. Berman has shown that if G is finite, then every unit of finite order is trivial if and only if G is abelian or the direct product of a quaternion group of order 8 and an elementary abelin 2-group. By comparison, Losey in [7] has shown that if ZG contains one non-trivial unit of finite order, then it contains infinitely many.

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