Zur Kinematik der isotropen Ebene

In this paper there are studied kinematics in the isotropic plane. We shall investigate fundamental properties of the pointpaths, develope a formula analog to the wellknown formula of Euler — Savary and study special motions: An isotropic elliptic motion and an isotropic four — bar — motion.     

Kreisgeometrie in der isotropen Ebene

Ohne ZusammenfassungHerrn K. Strubecker zum 60. Geburtstag gewidmet     

Zur Kinematik der isotropen Ebene II

In this paper there are studied mozions / _o in the isotropic plane. Given a C² — curve k in the moving frame we find the enveloped curve k_o in the fixed frame _o and consider the correspondance between the isotropic curvatures A and A_o of k and k_o. Than we investigate third-order properties of the pointpaths.     

Bemerkungen zum Satz von Abramescu in der euklidischen und der isotropen Ebene

Ohne Zusammenfassung     

Bögen der kinematischen Ordnung 2 in der isotropen Ebene

In this paper we try to characterise all arcs in the isotropic plane, that have not more than two points in common with any of their images under an isotropic motion.     

Ein Beispiel einer kinematisch induzierten Lieschen Kreisverwandtschaft der isotropen Ebene

We give a concrete example of a Lie-map in an isotropie plane which is neither a Möbius-map nor a Laguerre-map.     

A projective characterisation of ellipsoids by isotropy

In projective geometry, ellipsoids may be characterised by a property of isotropy about a single point. The author wishes to thank Rainer L?wen for advice on the presentation of the proof.     

Right distributive quasigroups on algebraic varieties

In this paper we develop a structure theory of algebraic right distributive quasigroups which correspond to closed and connected conjugacy classes generating algebraic Fischer groups (in the sense of [6]) such that the mappingx x ^–1 ax, fora , is an automorphism of (as variety). We also give examples of algebraic Fischer groups where this does not happen. It becomes clear that the class of algebraic right distributive quasigroups has nice properties concerning subquasigroups, normal subquasigroups and direct product.We give a complete classification of one- and two-dimensional as well as of minimal algebraic right distributive quasigroups.     

Ein projektiver Beweis für den Peripheriewinkelsatz und den Satz von den Tangentenstrecken in der isotropen Ebene

Ohne Zusammenfassung     

On combinatorial properties of spheres in euclidean spaces

For λ>√2 there exists a triangle-free graphG such that for nod canG be imbedded into thed-dimensional unit sphere with two points joined if and only if their distance is >λ.     

On the lattice formed by all normal subloops of a finite loop

All normal subloops of a loopG form a modular latticeL _n (G). It is shown that a finite loopG has a complemented normal subloop lattice if and only ifG is a direct product of simple subloops. In particular,L _n (G) is a Boolean algebra if and only if no two isomorphic factors occurring in a decomposition ofG are abelian groups. The normal subloop lattice of a finite loop is a projective geometry if and only ifG is an elementary abelianp-group for some primep.     

Die Automorphismen der isotropen Bewegungsgruppe

Ohne ZusammenfassungHerrn Professor K.Strubecker zum 60. Geburtstag     

Transversalenprobleme in der Ebene

Ohne ZusammenfassungDiese Arbeit ist ein Auszug aus der Dissertation des Verfassers (Göttingen 1969).