Reflection spaces, partial K-loops and K-loops
type: Item
instance of: scholarly article
title: Reflection spaces, partial K-loops and K-loops
zbMATH Open document ID: 1221.51016
author: Helmut Karzel
author: Sayed-Ghahreman Taherian
published in: Results in Mathematics
publication date: 2011-06-22T00:00:00Z
review text: The points in a reflection space are involutions in some group \(\Gamma\). A reflection space is called \(elliptic\) if there is a point \(p\) such that \(xp=px\) for some point \(x\neq p\). The authors show that in a non-elliptic reflection space any two distinct points have at most one midpoint. Moreover a transitive non-elliptic reflection space \(P\) is a regular permutation set. In order to get similar results for elliptic reflection spaces the authors assume the existence of a midpoint domain; they also introduce a partial \(K\)-loop with fibration.
Mathematics Subject Classification ID: 51F15
Mathematics Subject Classification ID: 20N05
zbMATH DE Number: 5911443
zbMATH Keywords: reflection space
zbMATH Keywords: reflection structure
zbMATH Keywords: \(K\)-loop
zbMATH Keywords: partial \(K\)-loop
reviewed by: Erich W. Ellers
MaRDI profile type: Publication
full work available at URL: s00025-010-0085-6
OpenAlex ID: W2050361843
cites work: Einbettung eines desarguesschen Ebenenkeimes in eine projektive Ebene
cites work: Q3998173
cites work: Q5662517
cites work: Elliptic reflection structures, K-loop derivations and triangle-inequality
cites work: Q4143823
cites work: Q4946739
cites work: Ein gruppentheoretischer Beweis des Satzes von Desargues in der absoluten Axiomatik
DOI: 10.1007/S00025-010-0085-6
description: scientific article; zbMATH DE number 5911443