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Introduction
Publications
Publications (41)
We give a rather elementary and short proof for the classification of finite nearfields, using Zsigmondy primes.
Lexicographic or first choice constructions of geometric objects sometimes
lead to amazingly good results. Usually it is difficult to determine the
precise identity of these geometries. Here we find infinitely many cases where
the identification actually can be accomplished.
Among three natural numbers there is always one which is larger than or equal
to the Nim sum of the remaining two numbers. This amazing fact has many
applications.
We describe a new way to construct finite geometric objects. For every
$k$
we obtain a symmetric configuration
$\mathcal{E }(k-1)$
with
$k$
points on a line. In particular, we have a constructive existence proof for such configurations. The method is very simple and purely geometric. It also produces interesting periodic matrices.
We describe a new way to construct finite geometric objects. For every k we
obtain a symmetric configuration E(k-1) with k points on a line. In particular,
we have a constructive existence proof for such configurations. The method is
very simple and purely geometric. It also produces interesting periodic
matrices.
We show that a maximal partial plane of order 6 with 31 lines and a maximal pure partial plane of order 6 with 25 lines can
be constructed from the icosahedron and the Petersen graph.
The purpose of this article is to give classification of semifields of order 54 admitting a free automorphism group E z2 × z2, and to find their kernels (left nuclei).
The purpose of this paper is to prove the existence of semifields of order q
4 for any odd prime power q = pr, q > 3, admitting a free automorphism group isomorphic to Z
2 × Z
2.
The purpose of this paper is to give a general and a simple approach to describe the Sylow r-subgroups of classical groups.
The finite nearfields can be classified using R. Brauer's result on finite linear groups whose orders are divisible by large primes, together with some elementary number theory.
An algorithm is devised to determine all solutions of any Diophantine equation of the type described in the title.
An algorithm is devised to determine all solutions of any Diophantine equation of the type described in the title.
An algorithm is devised to determine all solutions of any Diophantine equation of the type described in the title.
Collineation groups of finite projective planes are studied which do not leave invariant any point, line or triangle and contain a non-trivial perspectivity. In many instances the collineation group G can be determined, and it can be proved that the underlying projective plane contains a desarguesian subplane, whose order is related to the order of...
In this paper, we obtain information about the minimal degree δ of any non-trivial projective representation of the group PSL( n, q ) with n ≧ 2 over an arbitrary given field K. Our main results for the groups PSL( n , q ) (Theorems 4.2, 4.3, and 4.4) state that, apart from certain exceptional cases with small n , we have the following rather surpr...
Die Literatur fiber mehrfach transitive Permutationsgruppen entNilt viele Abhandlungen fiber die Beziehung zwischen den Eigenschaften einer Permutationsgruppe G und der maximalen Anzahl F(G) von Fixpunkten yon nichttrivialen Elementen aus G. Besonders fiber Gruppen G, ffir die die Invariante F(G) entweder sehr klein oder im Verhfiltnis zum Grad n v...
w 1. Einleitung Unter den Automorphismen einer M6bius-Ebene fallen zwei Klassen auf, deren Fixelemente besonders leicht flberschaubar angeordnet sind: Erstens Automorphismen, die genau einen Fixpunkt A haben und aul3erdem alle Kreise eines Beriihrbiischels b durch A fest lassen, und zweitens Automorphismen, die genau zwei Fixpunkte C und D haben un...
