Projektivitätengruppen von Ebenen über endlichen Semikörpern

Summary The group of projectivities of every finite non-desarguesian semi-field plane of odd order is the symmetric group. Similar results hold for groups of affine projectivities.

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Herrn Professor Joussen zum 60. Geburtstag gewidmet     

Strutture Di Andre Eds-Spazi Con Traslazioni

In this note we consider finite André structures possessing a sufficiently large number of translations. Results are obtained on the structure of the dilatation group and the group generated by central translations. The case of Sperner space is examined in detail.

     

Gruppen mit geometrischen Abschnitten im Untergruppenverband

Our aim is to analyse the influence of geometric properties which are valid in a section of the lattice of subgroups of an (abstract or topological) group on the structure of the group itself and to test thereby the applicability of genuine methods of synthetic geometry for algebraic purposes.

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Der zweite Autor bedankt sich für ein Stipendium von G.N.S.A.G.A. des C.N.R. (Italien).

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Der dritte Autor bedankt sich beim DAAD für ein Stipendium, das ihm den Aufenthalt an der Universität Erlange-Nürnberg ermöglicht hat.     

Finite Homomorphic Images of Groups of Finite Rank

Let π be a finite set of primes. We prove that each soluble group of finite rank contains a finite index subgroup whose every finite homomorphic π-image is nilpotent. A similar assertion is proved for a finitely generated group of finite rank. These statements are obtained as a consequence of the following result of the article: Each soluble pro-π-group of finite rank has an open normal pronilpotent subgroup.

     

Stark stetige Halbgruppen und Gruppen als Lösungen von Cauchy-Problemen in der Mathematischen Physik

The solution of an abstract Cauchy Problem in Mathematical Physics is either a strongly continuous group —then the problem is reversible—or a strongly continuous semigroup—then the problem is irreversible. Four examples are considered: The Schrödinger-, the wave-, the diffusion- and the linear transport equation.

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Mit 1 Abbildung

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Herrn Prof. Dr. E. Hlawka zum 60. Geburtstag gewidmet     

Die Normalteiler symplektischer Gruppen¶über Bewertungsringen mit einer¶Restklassenkörper-Charakteristik ≠ 2

In the present paper the normal subgroups of a symplectic group SP(L of a lattice L (not necessarily modular) over a valuation ring, whose residue class field has not characteristic 2, are characterised by an interval condition and the occuring intervals are described by the corresponding factor group given by the interval ends. This generalizes results of C. Riehm [7].

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Received: 8 September 1998     

Integral Ext2 Between Hook Weyl Modules

This paper concerns representations of the integral general linear group. The extension groups Ext² between any pair of hook Weyl modules are determined via a detailed study of cyclic generators and relations associated to certain extensions. As a corollary, the modular extension groups Ext¹ between such modules are determined.

     

Automorphism groups of causal symmetric spaces of Cayley type and bounded symmetric domains

Symmetric spaces of Cayley type are a higher dimensional analogue of a one-sheeted hyperboloid in ℝ³. They form an important class of causal symmetric spaces. To a symmetric space of Cayley type M, one can associate a bounded symmetric domain of tube type D. We determine the full causal automorphism group of M. This clarifies the relation between the causal automorphism group and the holomorphic automorphism group of D.

     

Semigroups generated by a group and an idempotent

It is well known that the semigroup of all transformations on a finite set X of order n is generated by its group of units, the symmetric group, and any idempotent of rank n ? 1. Similarly, the symmetric inverse semigroup on X is generated by its group of units and any idempotent of rank n ? 1 while the analogous result is true for the semigroup of all n × n matrices over a field.

In this paper we begin a systematic study of the structure of a semigroup S generated by its group G of units and an idempotent ? . The first section consists of preliminaries while the second contains some general results which provide the setting for those which follow.

In the third section we shall investigate the situation where G is a permutation group on a set X of order n and ? is an idempotent of rank n ? 1. In particular, we shall show that any such semigroup S is regular. Furthermore we shall determine when S is an inverse or orthodox semigroup or completely regular semigroup.

The fourth section deals with a special case, that in which G is cyclic. The fifth, and last, deals with the situation where G is dihedral. In both cases, the resulting semigroup has a particularly delicate structure which is of interest in its own right. Both situations are replete with interesting combinatorial gems.

The author was led to the results of this paper by considering the output of a computer program he was writing for generating and analyzing semigroups.     

Embeddings Determined by Universal Words in the Rank 2 Free Group

We consider a specific method for embedding a countable group that is given by generators and relations into some 2-generated group. This embedding enables us to express the images of generators of the countable group in the 2-generated group and explicitly deduce from the defining relations of the latter those of the former which inherit some special properties. The method can be used to construct the explicit embeddings of recursive groups into finitely presented groups.

     

Edgeworth Expansions for Centered Random Walks on Covering Graphs of Polynomial Volume Growth

Edgeworth expansions for random walks on covering graphs with groups of polynomial volume growths are obtained under a few natural assumptions. The coefficients appearing in this expansion depend on not only geometric features of the underlying graphs but also the modified harmonic embedding of the graph into a certain nilpotent Lie group. Moreover, we apply the rate of convergence in Trotter’s approximation theorem to establish the Berry–Esseen-type bound for the random walks.

     

STRONGLY PRIME GROUP RINGS

Abstract

A ring R is (right) strongly prime (SP) if every nonzero two sided ideal contains a finite set whose right annihilator is zero, SP rings have been studied by Handelman and Lawrence who raised the problem of characterizing SP group algebras. They showed that if R is SP and G is torsion free Abelian, then the group ring RG is SP. The aim of this note is to determine some more group rings which are SP.

For a ring R we also define the strongly prime radical s(R). We then show that s(R)G = s(W) for certain classes of groups.     

Lokal-Global-Prinzipien für die Brauergruppe

This article looks at Local-Global-Principles for the Brauer group, modeled after the celebrated theorem of Hasse-Brauer-Noether for the Brauer group of a number field. Pop introduced a property for fields, which holds especially for real closed andp-adically closed fields and yields a Local-Global-Principle for function fields of one variable over such fields. Then he used model theoretical means to generalize these results to arbitrary extensions of transcendental degree one over real closed andp-adically closed fields. This paper achieves this in a more elementary manner. Another result are examples of fields where the Local-Global-Principle is violated.

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This article was processed by the author using the IATEX style filecljour1 from Springer-Verlag.     

Halogen substituted amides

A CNDO calculation was carried out for N-methyl carbomyl chloride and N-chloroacetamide. The charges, bond orders, and dipolemoments of these molecules were calculated and the effect of chlorine substitution on amide group is discussed. The two highest filled M.O.s in both molecules are almost degenerate; they are a pi-orbital followed by the non-bonding oxygen lone pair orbital. In case of N-chloro acetamide the charges, bond orders and dipolemoments have been calculated for both cis and trans structures and the average dipolemoment calculated on the basis of infrared data and orbital calculation is reported.

     

Espaces de Besov et estimations de Strichartz généralisées sur le groupe de Heisenberg

In this paper, we prove dispersive and Strichartz inequalities on the Heisenberg group. The proof involves the analysis of Besov-type spaces on the Heisenberg group.

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Le travail du troisième auteur est partiellement finacé par la NNSF de Chine.     

Mod-retractable strongly π-regular rings and group algebras

Abstract

In this work, we show that a two-sided mod-retractable and strongly π-regular ring is two-sided semiartinian. On the other hand, a strongly π-regular von Neumann regular ring is left mod-retractable if and only if it is a left semiartinian V-ring. We apply these results to group algebras and thereby we give the complete structure of groups whose group algebras are mod-retractable.

Communicated by Toma Albu     

The Mathematics of Quantum Chemistry

A brief historical account of the use of wave mechanics in the field of theoretical chemistry leads to a consideration of three parts of mathematics that have been found particularly important. These are:

The use of Rayleigh's principle to obtain approximate eigenvalues and eigenfunctions.

The use of group theory, particularly the more familiar point groups, to classify electronic states of a molecule, and indicate which transitions are allowed.

The evaluation of the very complicated many‐centre integrals that are inescapable if acceptable numerical validity is desired. Finally reference is made to three other directions in which additional mathematical power would be of advantage to the theoretical chemist.     

Action du groupe des tresses sur une catégorie

We describe how to define by generators and relations an action of the braid group on a category. More generally, how to define a functor from a generalized positive braids monoid, corresponding to a finite Coxeter group, to a monoidal category. Applications to constructions of Bondal (exceptional systems) and of Broué–Michel (correspondences on flag manifolds) are given. 0. Introduction...159 1. Actions...164 2. Contractibilité...171 Bibliographie...175

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Oblatum: VII-1996     

A Simple Proof of the Riemann Mapping Theorem for Domains with Spherical Boundary

We give a simple proof of a Riemann mapping theorem for domains in a Stein manifold with a spherical boundary. Those boundaries are real hypersurfaces which are locally CR equivalent to the sphere inside complex space. The main observation is that for higher dimensional Stein manifolds, the fundamental group of its boundary coincides with that of its interior.