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Displaying 81 – 100 of 126

Sylow P-Subgroups of Abelian Group Rings

Danchev, P. (2003)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary 20C07, 20K10, 20K20, 20K21; Secondary 16U60, 16S34.Let PG be the abelian modular group ring of the abelian group G over the abelian ring P with 1 and prime char P = p. In the present article,the p-primary components Up(PG) and S(PG) of the groups of units U(PG) and V(PG) are classified for some major classes of abelian groups. Suppose K is a first kind field with respect to p in char K ≠ p and A is an abelian p-group. In the present work, the p-primary...

Symmetric units and group identities in group algebras. I.

Bovdi, Victor (2006)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

The adjoint representation of group algebras and enveloping algebras.

Donald S. Passman (1992)

Publicacions Matemàtiques

In this paper we study the Hopf adjoint action of group algebras and enveloping algebras. We are particularly concerned with determining when these representations are faithful. Delta methods allow us to reduce the problem to certain better behaved subalgebras. Nevertheless, the problem remains open in the finite group and finite-dimensional Lie algebra cases.

The based ring of the lowest two-sided cell of an affine Weyl group. II

Nanhua Xi (1994)

Annales scientifiques de l'École Normale Supérieure

The Bass conjecture and growth in groups

Anders Karlsson, Markus Neuhauser (2004)

Colloquium Mathematicae

We discuss Bass's conjecture on the vanishing of the Hattori-Stallings rank from the viewpoint of geometric group theory. It is noted that groups without u-elements satisfy this conjecture. This leads in particular to a simple proof of the conjecture in the case of groups of subexponential growth.

The centre of completed group algebras of pro- $p$ groups.

Ardakov, Konstantin (2004)

Documenta Mathematica

The Equivalence of Various Generalizations of Group Rings and Modules.

Everett C. Dade (1982)

Mathematische Zeitschrift

The Heart of Prime Ideals in Ore Extensions.

Martin Lorenz (1979)

Manuscripta mathematica

The isomorphic description of torsion units in commutative group rings over fields with positive characteristic.

Danchev, Peter (2004)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

The rank of G0 for polycyclic group algebras

M. Lorenz (1990)

Banach Center Publications

The upper central series of some matrix groups

B. Wehrfritz (1990)

Fundamenta Mathematicae

Torsion units in group rings.

Vikas Bist (1992)

Publicacions Matemàtiques

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.

Trivial units in commutative group algebras.

P. Danchev (2008)

Extracta Mathematicae

Two properties of the filtration of the outer automorphism groups of certain groups.

Mamoru Asada (1995)

Mathematische Zeitschrift

Unitary subgroup of integral groups rings.

S.K. Sehgal, A.A. Bovdi (1992)

Manuscripta mathematica

Unitary units in modular group algebras.

L.G. Kovács, Victor Bovdi (1994)

Manuscripta mathematica

Units in group rings of crystallographic groups

Karel Dekimpe (2003)

Fundamenta Mathematicae

In [3], the authors initiated a technique of using affine representations to study the groups of units of integral group rings of crystallographic groups. In this paper, we use this approach for some special classes of crystallographic groups. For a first class of groups we obtain a normal complement for the group inside the group of normalized units. For a second class of groups we show that the Zassenhaus conjectures ZC1 and ZC3 are valid. This generalizes the results known for the infinite dihedral...

Valuations and group algebras

Ulrich Albrecht, Günter Törner (1998)

Rendiconti del Seminario Matematico della Università di Padova

Warfield Invariants in Abelian Group Algebras

Peter Danchev (2008)

Collectanea Mathematica

Warfield invariants in abelian group rings.

Peter V. Danchev (2005)

Extracta Mathematicae

Let R be a perfect commutative unital ring without zero divisors of char(R) = p and let G be a multiplicative abelian group. Then the Warfield p-invariants of the normed unit group V (RG) are computed only in terms of R and G. These cardinal-to-ordinal functions, combined with the Ulm-Kaplansky p-invariants, completely determine the structure of V (RG) whenever G is a Warfield p-mixed group.

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