Geodesic
A Class of Homomorphisms of Pre-Hjelmslev Groups
Canadian journal of mathematics, Tome 36 (1984) no. 3, pp. 470-494

Voir la notice de l'article provenant de la source Cambridge University Press

E. Salow [8] introduced the concept of pre-Hjelmslev groups, a generalization of F. Bachmann's Hjelmslev groups [1] which leads to a more natural theory of homomorphisms and permits a simpler construction of algebraic models. Basically, both types of groups are the groups of motions of a metric plane, the so-called group plane. In such a plane there is a unique perpendicular through any point to any line and the product of three collinear points (three copunctal lines) is a point (a line). Our first section contains the precise definitions and some basic facts.The homomorphic image of a pre-Hjelmslev group can be more complicated than the pre-image. For instance, there may always be a unique line through two distinct points of the pre-image but not of the image. We study regular homomorphisms of pre-Hjelmslev groups, i.e., homomorphisms with the following property: If two lines intersect at exactly one point, their images will also have precisely one point in common. 
Knüppel, Frieder. A Class of Homomorphisms of Pre-Hjelmslev Groups. Canadian journal of mathematics, Tome 36 (1984) no. 3, pp. 470-494. doi: 10.4153/CJM-1984-029-4
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