scholarly journals Groups generated by two bicyclic units in integral group rings

2002 ◽  
Vol 5 (4) ◽  
Author(s):  
Eric Jespers ◽  
ángel del Río ◽  
Manuel Ruiz
Keyword(s):  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings ◽  
Bicyclic Units

Bicyclic Units in some Integral Group Rings

1995 ◽  
Vol 38 (1) ◽  
pp. 80-86 ◽  
Author(s):  
E. Jespers
Keyword(s):  
Finite Index ◽  
Unit Group ◽  
Group Rings ◽  
Integral Group ◽  
Normal Complement ◽  
Integral Group Rings ◽  
Torsion Free ◽  
Bicyclic Units

AbstractA description is given of the unit group for the two groups G = D12 and G = D8 × C2. In particular, it is shown that in both cases the bicyclic units generate a torsion-free normal complement. It follows that the Bass-cyclic units together with the bicyclic units generate a subgroup of finite index in for all n ≥ 3.

scholarly journals Gauss Units in Integral Group Rings

1998 ◽  
Vol 204 (2) ◽  
pp. 588-596 ◽  
Author(s):  
Olaf Neisse ◽  
Sudarshan K. Sehgal
Keyword(s):  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings

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.

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