S. O. Juriaans

SOME STRUCTURAL PROPERTIES OF THE TOPOLOGICAL RING OF COLOMBEAU'S GENERALIZED NUMBERS

Let denote the commutative ring with identity of Colombeaus generalized numbers. (K will denote either R or C). This ring can be endowed with an ultra-metric in such a way that is a topological ring. There are many interesting questions about in the frameworks of Commutative Algebra and General Topology as well as of the superposition of these two subjects. This paper is meant to represent an initial step in this direction. In a few simple cases the study is extended to the ring of Colombeaus generalized functions on an open subset of R n .

Automorphisms of Finite Groups

Abstract We study the classification of those finite groups G having a non-inner class preserving automorphism. Criteria for these automorphisms to be inner are established. Let G be a nilpotent-by-nilpotent group and S ∈ Sy l 2(G). If S is abelian, generalized quaternion or S is dihedral, and in this case G is also metabelian, then Out c (G) = 1. If S is generalized quaternion, 𝒵(S) ⊂ 𝒵(G) and S 4 is not a homomorphic image of G, then Out c (G) = 1. As a consequence, it follows that the normalizer problem of group rings has a positive answer for these groups.

Hyperbolic unit groups

In this paper we study the groups G whose integral group rings have hyperbolic unit groups U(ZG). We classify completely the torsion subgroups of U(ZG) and the polycyclic-by-finite subgroups of the group G. Finally, we classify the groups for which the boundary of U(ZG) has dimension zero.

From the Poincaré Theorem to generators of the unit group of integral group rings of finite groups

We give an algorithm to determine finitely many generators for a subgroup of finite index in the unit group of an integral group ring

On hypercentral units in integral group rings

\mathbb{Z} G

HYPERCENTRAL UNIT GROUPS AND THE HYPERBOLICITY OF A MODULAR GROUP ALGEBRA

of a finite nilpotent group

HYPERBOLICITY OF SEMIGROUP ALGEBRAS II

G

Traces of Torsion Units

, this provided the rational group algebra

EXTENSION OF AUTOMORPHISMS OF SUBGROUPS

\mathbb{Q} G

Polynomial Identities of RA and RA2 Loop Algebras

does not have simple components that are division classical quaternion algebras or two-by-two matrices over a classical quaternion algebra with centre