Coeuklidische Hjelmslevgruppen. (On co-Euclidean Hjelmslev groups)
type: Item
instance of: scholarly article
title: Coeuklidische Hjelmslevgruppen. (On co-Euclidean Hjelmslev groups)
zbMATH Open document ID: 0667.51006
DOI: 10.1007/BF01224243
author: Horst Struve
author: Rolf Struve
published in: Journal of Geometry
publication date: 1989-01-01T00:00:00Z
review text: A 3-dimensional metric vector space V over a field of characteristic \(\neq 2\) defines a reflection geometry in the sense of F. Bachmann, i.e., a geometry of line reflections in an orthogonal group. The case \(Ind V=0,\) \(\dim rad V=1\) is dealt with in this paper. It is treated as one out of four possible geometries which are all covered by a general characterization of co-Euclidean Hjelmslev groups.
Mathematics Subject Classification ID: 51F15
Mathematics Subject Classification ID: 15A63
zbMATH DE Number: 4092232
zbMATH Keywords: metric vector space
zbMATH Keywords: line reflections
zbMATH Keywords: orthogonal group
zbMATH Keywords: Hjelmslev groups
reviewed by: Ferdinand D. Veldkamp
MaRDI profile type: Publication
cites work: Q3852754
cites work: Trägheitssatz und halbelliptische Bewegungsgruppen
cites work: Die Ordnungsfunktionen einer Geometrie
cites work: Ein spiegelungsgeometrischer Aufbau der cominkowskischen Geometrie
cites work: Hjelmslevgruppen, in denen sich die Punkte gegen Geraden austauschen lassen
cites work: Minkowskische und absolute Geometrie. I, II
full work available at URL: https://doi.org/10.1007/bf01224243
OpenAlex ID: W4255376636
description: scientific article; zbMATH DE number 4092232