scholarly journals Picard groups and automorphism groups of integral group rings of metacyclic groups

1982 ◽  
Vol 77 (2) ◽  
pp. 286-310 ◽  
Author(s):  
Shizuo Endo ◽  
Takehiko Miyata ◽  
Katsusuke Sekiguchi
Keyword(s):  
Automorphism Groups ◽  
Group Rings ◽  
Integral Group ◽  
Metacyclic Groups ◽  
Integral Group Rings ◽  
Picard Groups

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.

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

Units of Integral Group Rings of Some Metacyclic Groups

1994 ◽  
Vol 37 (2) ◽  
pp. 228-237 ◽  
Author(s):  
Eric Jespers ◽  
Guilherme Leal ◽  
C. Polcino Milies
Keyword(s):  
Finite Index ◽  
Unit Group ◽  
Group Algebras ◽  
Group Rings ◽  
Integral Group ◽  
Rational Group ◽  
Metacyclic Groups ◽  
Integral Group Rings ◽  
Almost All ◽  
Natural Way

AbstractIn this paper, we consider all metacyclic groups of the type 〈a,b | an - 1, b2 = 1, ba = aib〉 and give a concrete description of their rational group algebras. As a consequence we obtain, in a natural way, units which generate a subgroup of finite index in the full unit group, for almost all such groups.

scholarly journals TORSION UNITS IN INTEGRAL GROUP RINGS OF CERTAIN METABELIAN GROUPS

2008 ◽  
Vol 51 (2) ◽  
pp. 363-385 ◽  
Author(s):  
Martin Hertweck
Keyword(s):  
Finite Group ◽  
Abelian Group ◽  
Group Rings ◽  
Integral Group ◽  
Metabelian Groups ◽  
Metacyclic Groups ◽  
Integral Group Rings ◽  
Torsion Unit ◽  
A Finite Group ◽  
Torsion Units

AbstractIt is shown that any torsion unit of the integral group ring $\mathbb{Z}G$ of a finite group $G$ is rationally conjugate to an element of $\pm G$ if $G=XA$ with $A$ a cyclic normal subgroup of $G$ and $X$ an abelian group (thus confirming a conjecture of Zassenhaus for this particular class of groups, which comprises the class of metacyclic groups).

Sign in / Sign up

Export Citation Format

Share Document