Special Quasi-triads and Integral Group Rings of Finite Representation Type, I

On Torsion Subgroups in Integral Group Rings of Finite Groups

Quasi-Complete Primary Components in Modular Abelian Group Rings over Special Rings

Let G be a multiplicatively written p-separable abelian group and R a commutative unitary ring of prime characteristic p so that Rp i has nilpotent elements for each positive integer i > 1. Then, we prove that, the normed unit p-subgroup S(RG) of the group ring RG is quasi-complete if and only if G is a bounded p-group. This strengthens our recent results in (Internat. J. Math. Analysis, 2006) ...

Rational Group Algebras of Finite Groups: from Idempotents to Units of Integral Group Rings

We give an explicit and character-free construction of a complete set of orthogonal primitive idempotents of a rational group algebra of a finite nilpotent group and a full description of the Wedderburn decomposition of such algebras. An immediate consequence is a well-known result of Roquette on the Schur indices of the simple components of group algebras of finite nilpotent groups. As an appl...

D-modules over Rings with Finite F-representation Type

Smith and Van den Bergh [29] introduced the notion of finite F-representation type as a characteristic p analogue of the notion of finite representation type. In this paper, we prove two finiteness properties of rings with finite F-representation type. The first property states that if R = L n≥0 Rn is a Noetherian graded ring with finite (graded) F-representation type, then for every non-zerodi...

Unit Groups of Integral Finite Group Rings with No Noncyclic Abelian Finite Subgroups

It is shown that in the units of augmentation one of an integral group ring ZG of a finite group G, a noncyclic subgroup of order p, for some odd prime p, exists only if such a subgroup exists in G. The corresponding statement for p = 2 holds by the Brauer–Suzuki theorem, as recently observed by W. Kimmerle.