Results 231 to 240 of about 1,766,233 (264)

Unit Groups of Group Rings

1999
For a commutative ring R with identity and an arbitrary group G, let RG denote the group ring of G over R and U(RG) its group of units. It is of interest, see the survey by Dennis (1977), to determine the necessary and sufficient conditions on R and G in order that U(RG) has a specific group-theoretic property, e.g., solvability, nilpotence, etc ...
Ashwani K. Bhandari, I. B. S. Passi
openaire   +1 more source

ON THE DERIVED LENGTH OF THE GROUP OF UNITS OF A GROUP ALGEBRA

Journal of Algebra and Its Applications, 2007
Let G be a group with cyclic derived subgroup of p-power order (p > 2), and F a field of characteristic p. We determine the derived length of the group of units of the group algebra FG.
Balogh, Zsolt, Li, Yuanlin
openaire   +1 more source

On the derived length of the unit group of a group algebra

Journal of Group Theory, 2010
Let \(KG\) be the group algebra of the torsion nilpotent group \(G\) over the field \(K\) of positive charateristic \(p\) with the unit group \(U(KG)\) solvable. Conditions under which the unit group is solvable were investigated by several authors in various cases, but little is known about the derived length of the unit group. \textit{C.
CATINO, Francesco, Ernesto SPINELLI
openaire   +4 more sources

Group Identities on Units and Symmetric Units of Group Rings

2010
Group Identities on Units of Group Rings.- Group Identities on Symmetric Units.- Lie Identities on Symmetric Elements.- Nilpotence of ...
openaire   +1 more source

The unit group of the modular small group algebra

Mathematical Journal of Okayama University, 1995
Let \(G\) be a finite \(p\)-group whose commutator subgroup is elementary Abelian and \(F\) be the field of \(p\) elements. Denote by \(FG\) the group ring and by \(I(G)\) the kernel of the augmentation mapping. Denote by \(G_2\) the commutator subgroup of \(G\).
Salim, Mohamed A.M., Sandling, Robert
openaire   +3 more sources

BASS CYCLIC UNITS AS FACTORS IN A FREE GROUP IN INTEGRAL GROUP RING UNITS

International Journal of Algebra and Computation, 2011
Marciniak and Sehgal showed that if u is a non-trivial bicyclic unit of an integral group ring then there is a bicyclic unit v such that u and v generate a non-abelian free group. A similar result does not hold for Bass cyclic units of infinite order based on non-central elements as some of them have finite order modulo the center.
Jairo Z. Gonçalves, Ángel del Río
openaire   +1 more source

Units in Group Rings of the Infinite Dihedral Group

Canadian Mathematical Bulletin, 1991
AbstractThis paper studies the group of units U(RD∞) of the group ring of the infinite dihedral group D∞ over a commutative integral domain R. The structures of U(Z2D∞) and U(Z3D∞) are determined, and it is shown that U(ZD∞) is not finitely generated.
openaire   +2 more sources

The group of units of a group algebra of characteristic $p$

Publicationes Mathematicae Debrecen, 1998
This is a rather long survey paper on the structure of the group of units of a group algebra \(\mathbb{F} G\) over a field \(\mathbb{F}\) of characteristic \(p\) and a (mostly infinite) group \(G\). The paper contains no proofs, but it contains a wealth of results and open problems.
openaire   +1 more source

Group rings in which the group of units is hyperbolic

jgth, 2012
Abstract. We study those group rings in which the group of units is hyperbolic.
openaire   +1 more source

Distribution of motor unit properties across human muscles

Journal of Applied Physiology, 2022
Jacques Duchateau, Roger M. Enoka
exaly