4-dimensionale projektive Ebenen vom Lenz-Barlotti-Typ II.2. (Four- dimensional projective planes of Lenz-Barlotti type II.2.)
type: Item
instance of: scholarly article
title: 4-dimensionale projektive Ebenen vom Lenz-Barlotti-Typ II.2. (Four- dimensional projective planes of Lenz-Barlotti type II.2.)
zbMATH Open document ID: 0626.51011
DOI: 10.1007/BF03322384
author: Norbert Knarr
published in: Results in Mathematics
publication date: 1987-01-01T00:00:00Z
review text: A topological projective plane is called flexible if its collineation group has an open orbit in the flag space. A projective plane \(\pi\) is of Lenz-Barlotti type II.2 if it contains points u, v and lines S, W with \(v=W\wedge S\) and \(u\in W\setminus \{v\}\) such that \(\pi\) is (u,S)- and (w,W)-transitive and has no further (point, line)-transitivities. The author now determines all flexible 4-dimensional projective planes of Lenz-Barlotti type II.2. Every projective plane of this Lenz-Barlotti type is coordinatizable by a planar double group, and in the case treated here its additive and multiplicative groups are isomorphic to those of the complex field, respectively. Alternatively, these planes are shown to be characterized as those flexible 4-dimensional projective planes whose collineation group contains a subgroup isomorphic to \({\mathbb{R}}^ 3\times SO_ 2\).
Mathematics Subject Classification ID: 51H10
Mathematics Subject Classification ID: 51A25
zbMATH DE Number: 4017751
zbMATH Keywords: flexible 4-dimensional projective planes of Lenz-Barlotti type
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4017751