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Displaying 21 – 40 of 126

Commutative modular group algebras of $p$ -mixed and $p$ -splitting abelian $Σ$ -groups

Peter Vassilev Danchev (2002)

Commentationes Mathematicae Universitatis Carolinae

Let $G$ be a $p$ -mixed abelian group and $R$ is a commutative perfect integral domain of $char R = p > 0$ . Then, the first main result is that the group of all normalized invertible elements $V (R G)$ is a $Σ$ -group if and only if $G$ is a $Σ$ -group. In particular, the second central result is that if $G$ is a $Σ$ -group, the $R$ -algebras isomorphism $R A ≅ R G$ between the group algebras $R A$ and $R G$ for an arbitrary but fixed group $A$ implies $A$ is a $p$ -mixed abelian $Σ$ -group and even more that the high subgroups of $A$ and $G$ are isomorphic, namely, $ℋ_{A} ≅ ℋ_{G}$ . Besides,...

Complete radicals of some group rings.

Kornev, A.I. (2007)

Sibirskij Matematicheskij Zhurnal

Cuspidal local systems and graded Hecke algebras, I

George Lusztig (1988)

Publications Mathématiques de l'IHÉS

Cyclic homology of groups and the Bass conjecture.

Bruno Eckmann (1986)

Commentarii mathematici Helvetici

Dimension sugroups of metabelian groups.

N.D. Gupta, A.W. Hales, I.B.S. Passi (1984)

Journal für die reine und angewandte Mathematik

Direct decompositions and basic subgroups in commutative group rings

Peter Vassilev Danchev (2006)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

An attractive interplay between the direct decompositions and the explicit form of basic subgroups in group rings of abelian groups over a commutative unitary ring are established. In particular, as a consequence, we give a simpler confirmation of a more general version of our recent result in this aspect published in Czechoslovak Math. J. (2006).

Direct finiteness of group rings - a simple proof of the Kaplansky's conjecture for finite groups

Jan Trlifaj (1990)

Commentationes Mathematicae Universitatis Carolinae

Extensions of abelian by hyper-(cyclic or finite) groups (II)

Z. Y. Duan (1993)

Rendiconti del Seminario Matematico della Università di Padova

Faithful integral and modular representations of the Klein bottle group

Hugo H. Torriani (1987)

Colloquium Mathematicae

Free pro-p groups with operators.

B. Baumann (1991)

Manuscripta mathematica

$G$ -nilpotent units of commutative group rings

Peter Vassilev Danchev (2012)

Commentationes Mathematicae Universitatis Carolinae

Suppose $R$ is a commutative unital ring and $G$ is an abelian group. We give a general criterion only in terms of $R$ and $G$ when all normalized units in the commutative group ring $R G$ are $G$ -nilpotent. This extends recent results published in [Extracta Math., 2008–2009] and [Ann. Sci. Math. Québec, 2009].

Generalised Magnus modules over the braid group.

Mirko Lüdde (1996)

Mathematische Annalen

Generalizations of morphic group rings.

Zan, Libo, Chen, Jianlong, Huang, Qinghe (2007)

International Journal of Mathematics and Mathematical Sciences

Group algebras of abelian groups

Donna Beers, Fred Richman, Elbert A. Walker (1983)

Rendiconti del Seminario Matematico della Università di Padova

Group rings and irreducible representations of space groups.

W. Plesken, W. Hanrath (1985)

Journal für die reine und angewandte Mathematik

Group rings with FC-nilpotent unit groups.

Vikas Bist (1991)

Publicacions Matemàtiques

Let U(RG) be the unit group of the group ring RG. Groups G such that U(RG) is FC-nilpotent are determined, where R is the ring of integers Z or a field K of characteristic zero.

Group Rings with Units Torsion Over the Center.

S.K. Sehgal, G.H. Cliff (1980/1981)

Manuscripta mathematica

Homology of gaussian groups

Patrick Dehornoy, Yves Lafont (2003)

Annales de l’institut Fourier

We describe new combinatorial methods for constructing explicit free resolutions of $ℤ$ by $ℤ G$ -modules when $G$ is a group of fractions of a monoid where enough lest common multiples exist (“locally Gaussian monoid”), and therefore, for computing the homology of $G$ . Our constructions apply in particular to all Artin-Tits groups of finite Coexter type. Technically, the proofs rely on the properties of least common multiples in a monoid.

Homomorphisms of group rings

Jan Krempa (1982)

Banach Center Publications

Idempotents in complex group rings: Theorems of Zalesskij and Bass revisited.

Burger, Marc, Valette, Alain (1998)

Journal of Lie Theory

Currently displaying 21 – 40 of 126

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