4-transitivity and cross-ratio in Moufang-Klingenberg planes over rings of plural numbers
type: Item
instance of: scholarly article
title: 4-transitivity and cross-ratio in Moufang-Klingenberg planes over rings of plural numbers
zbMATH Open document ID: 1464.51007
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2021-05-05T00:00:00Z
review text: It is proved that the collineation group \(\mathcal{G}\) in the Moufang-Klingenberg plane \(\mathbb{M}(\mathcal{A})\), with \(\mathcal{A}\) the local ring of plural numbers \(\mathcal{A}:=\mathbb{O}[\eta]/\langle \eta^m \rangle\) over a Cayley division algebra \(\mathbb{O}\), acts transitively on the set of 4-gons. Also the cross-ratio of four distinct points on a line in \(\mathbb{M}(\mathcal{A})\) is discussed, inspired by work of \textit{A. Blunck} [Result. Math. 19, No 3--4, 246--256 (1991; Zbl 0725.51001); Geom. Dedicata 43, No 1, 93--107 (1992; Zbl 0758.51005)].
Mathematics Subject Classification ID: 51C05
zbMATH DE Number: 7344133
zbMATH Keywords: Moufang-Klingenberg plane
zbMATH Keywords: 4-transitivity
zbMATH Keywords: cross-ratio
zbMATH Keywords: local ring
author: Fatma O. Erdogan
reviewed by: Dirk Keppens
MaRDI profile type: Publication
full work available at URL: s13226-020-0474-9
OpenAlex ID: W3120308215
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DOI: 10.1007/S13226-020-0474-9
description: scientific article; zbMATH DE number 7344133