Geodesic
Neighbor Relation and Neighbor Homomorphism of Hjelmslev Groups
Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 680-699

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

The geometry of Hjelmslev groups is a comprehensive plane metric geometry. It supplies, for example, an approach to euclidean, hyperbolic, elliptic, Minkowskian and Galilean geometry.The subject of this geometry are Hjelmslev groups and their group planes. (The definition of Hjelmslev groups and some basic concepts and propositions of this theory can be found in the second edition of Bachmann's book [1] (pages 318-328). A similar report in English is the lecture [3]. A comprehensive introduction is developed in the key work [2]. The first part of this work was translated by Garner [4]. An abstract is given in Math. Rev. 52, 9066 (1976).) The group plane arises from giving geometric names to some group theoretical facts. The group plane of a Hjelmslev group is an incidence structure with orthogonality, and the Hjelmslev group acts on this plane as a group of motions. 
Knüppel, Frieder; Kunze, Michael. Neighbor Relation and Neighbor Homomorphism of Hjelmslev Groups. Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 680-699. doi: 10.4153/CJM-1979-068-5
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