Reflection spaces and corresponding kinematic structures
type: Item
instance of: scholarly article
title: Reflection spaces and corresponding kinematic structures
zbMATH Open document ID: 1263.51008
author: Sayed-Ghahreman Taherian
author: Helmut Karzel
published in: Results in Mathematics
publication date: 2013-02-08T00:00:00Z
review text: A reflection space is a pair \((P,\Gamma)\), where \(\Gamma\) is a group and \(P\) is a non-empty set of involutions in \(\Gamma\) that generates \(\Gamma\), satisfying a number of conditions, e.g. the three reflection axiom. These conditions give the pair \((P,\Gamma)\) a geometric structure. The authors of this paper investigate properties of this geometric structure. In particular they look at the collineation group of a reflection space, at reducible reflection spaces and their kinematic spaces, and at the kinematic structure of a reflection space.
reviewed by: Erich W. Ellers
Mathematics Subject Classification ID: 51F15
Mathematics Subject Classification ID: 51M10
Mathematics Subject Classification ID: 51G05
zbMATH DE Number: 6135269
zbMATH Keywords: reflection space
zbMATH Keywords: kinematic space
zbMATH Keywords: incidence group
zbMATH Keywords: reducible set
zbMATH Keywords: v-subgroup
MaRDI profile type: Publication
full work available at URL: s00025-011-0220-z
OpenAlex ID: W2046929233
cites work: Q5662517
cites work: Q4771790
cites work: Reflection spaces, partial K-loops and K-loops
cites work: Ein gruppentheoretischer Beweis des Satzes von Desargues in der absoluten Axiomatik
DOI: 10.1007/S00025-011-0220-Z
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description: scientific article; zbMATH DE number 6135269