3,312 research outputs found
On the isomorphism problem for unit groups of modular group algebras
Using the computational algebra system GAP (http://www.gap-system.org) and
the GAP package LAGUNA (http://www.cs.st-andrews.ac.uk/~alexk/laguna.htm), we
checked that all 2-groups of order not greater than 32 are determined by
normalized unit groups of their modular group algebras over the field of two
elements.Comment: 6 pages, accepted in Acta Sci. Math. (Szeged
Kimmerle conjecture for the Held and O'Nan sporadic simple groups
Using the Luthar--Passi method, we investigate the Zassenhaus and Kimmerle
conjectures for normalized unit groups of integral group rings of the Held and
O'Nan sporadic simple groups. We confirm the Kimmerle conjecture for the Held
simple group and also derive for both groups some extra information relevant to
the classical Zassenhaus conjecture.Comment: 9 page
Integral group ring of the first Mathieu simple group
We investigate the classical Zassenhaus conjecture for the normalized unit group
of the integral group ring of the simple Mathieu group M11. As a consequence, for
this group we confirm the conjecture by Kimmerle about prime graphs
Integral group ring of the McLaughlin simple group
We consider the Zassenhaus conjecture for the normalized unit group of the integral group ring of the McLaughlin sporadic group McL. As a consequence, we confirm for this group the Kimmerle’s conjecture on prime graphs
Kimmerle conjecture for the Held and O'Nan sporadic simple groups
Using the Luthar--Passi method, we investigate the Zassenhaus and
Kimmerle conjectures for normalized unit groups of integral group rings of the
Held and O'Nan sporadic simple groups. We confirm the Kimmerle conjecture for
the Held simple group and also derive for both groups some extra information
relevant to the classical Zassenhaus conjecture
Torsion units in integral group rings of Janko simple groups
Using the Luthar--Passi method, we investigate the classical Zassenhaus
conjecture for the normalized unit group of integral group rings of Janko
sporadic simple groups. As a consequence, we obtain that the Gruenberg-Kegel
graph of the Janko groups , and is the same as that of the
normalized unit group of their respective integral group ring.Comment: 23 pages, to appear in Math.Comp
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