The structure of the unit group of the group algebra
The structure of the unit group of the group algebra of the group over any finite field of characteristic 2 is established in terms of split extensions of cyclic groups.
The unit group of .
The upper central series of some matrix groups
Théorème de densité de Tchebotareff et monogénéité de modules sur l'algèbre d'un groupe métacyclique
Thick subcategories of the stable module category
We study the thick subcategories of the stable category of finitely generated modules for the principal block of the group algebra of a finite group G over a field of characteristic p. In case G is a p-group we obtain a complete classification of the thick subcategories. The same classification works whenever the nucleus of the cohomology variety is zero. In case the nucleus is nonzero, we describe some examples which lead us to believe that there are always infinitely many thick subcategories concentrated...
Torsion matrices over commutative integral group rings.
Let ZA be the integral group ring of a finite abelian group A, and n a positive integer greater than 5. We provide conditions on n and A under which every torsion matrix U, with identity augmentation, in GLn(ZA) is conjugate in GLn(QA) to a diagonal matrix with group elements on the diagonal. When A is infinite, we show that under similar conditions, U has a group trace and is stably conjugate to such a diagonal matrix.
Torsion units for some almost simple groups
We investigate the Zassenhaus conjecture regarding rational conjugacy of torsion units in integral group rings for certain automorphism groups of simple groups. Recently, many new restrictions on partial augmentations for torsion units of integral group rings have improved the effectiveness of the Luther-Passi method for verifying the Zassenhaus conjecture for certain groups. We prove that the Zassenhaus conjecture is true for the automorphism group of the simple group . Additionally we prove that...
Torsion units in group rings.
Let U(RG) be the unit group of the group ring RG. In this paper we study group rings RG whose support elements of every torsion unit are torsion, where R is either the ring of integers Z or a field K.
Torsion units in integral group rings.
Trivial units in commutative group algebras.
Two examples of inverse semigroups algebras.