Compact 16-dimensional projective planes with large collineation groups. III
type: Item
instance of: scholarly article
title: Compact 16-dimensional projective planes with large collineation groups. III
zbMATH Open document ID: 0544.51012
DOI: 10.1007/BF01181689
published in: Mathematische Zeitschrift
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173392
review text: [Part II, cf. Monat. Math. 95, 311-319 (1983; Zbl 0507.51009]. Let \({\mathcal P}\) be a topological projective plane whose point space is compact and has (covering) dimension 16. Denote by aut \({\mathcal P}\) the group of all continuous collineations, given the compact-open topology. Theorem: If \(\dim\;aut{\mathcal P}\geq 40\), then \({\mathcal P}\) is the classical Moufang plane over the real octonion algebra, or the fixed element configuration of aut \({\mathcal P}\) is a flag (incident point-line pair).
reviewed by: Hansjoachim Groh
Mathematics Subject Classification ID: 51H10
Mathematics Subject Classification ID: 54H15
zbMATH DE Number: 3866078
zbMATH Keywords: topological projective plane
zbMATH Keywords: collineation group
zbMATH Keywords: Moufang plane
author: Helmut Salzmann
MaRDI profile type: Publication
cites work: Lie Group Actions on a Cayley Projective Plane and a Note on Homogeneous Spaces of Prime Euler Characteristic
cites work: Q4156946
cites work: Zur Klassifikation von 8- und 16-dimensionalen lokalkompakten Translationsebenen nach ihren Kollineationsgruppen
cites work: Topology and dimension of stable planes: On a conjecture of H. Freudenthal.
cites work: Collineation groups of compact connected projective planes
cites work: Groups acting on the 4-sphere
cites work: Kollineationsgruppen kompakter, vier-dimensionaler Ebenen
cites work: Homogene kompakte projektive Ebenen
cites work: Compact 8-dimensional projective planes with large collineation groups
cites work: Automorphismengruppen 8-dimensionaler Ternärkörper
cites work: Kompakte, 8-dimensionale projektive Ebenen mit großer Kollineationsgruppe
cites work: Baer-Kollineationsgruppen der klassischen projektiven Ebenen
cites work: Compact 16-dimensional projective planes with large collineation groups
cites work: Compact 16-dimensional projective planes with large collineation groups. II
cites work: New results and old problems in finite transformation groups
cites work: Tabellen zu den einfachen Lie Gruppen und ihren Darstellungen
cites work: Transitivitätsfragen bei linearen Liegruppen
OpenAlex ID: W2091117068
description: scientific article; zbMATH DE number 3866078