Compact 16-dimensional projective planes
type: Item
instance of: scholarly article
title: Compact 16-dimensional projective planes
zbMATH Open document ID: 0933.51008
DOI: 10.1007/BF03322032
published in: Results in Mathematics
publication date: 2000-03-26T00:00:00Z
review text: The author continues his study of \(16\)-dimensional compact projective planes with large groups of automorphisms. It is shown that the existence of a group \(\Delta\) of automorphisms with \(\dim\Delta=39\) such that \(\Delta\) fixes more than one point implies that the plane is a translation plane. Then one knows that the plane is coordinatized by a so-called perturbation of the octonions [see 82.4 in \textit{H. Salzmann} et al., `Compact projective planes' (1995; Zbl 0851.51003)]. The proof in the present paper uses previous results that imply that \(\Delta\) contains a normal vector group. A detailed study of the linear representation of \(\Delta\) on this vector group yields the theorem.
Mathematics Subject Classification ID: 51H10
zbMATH DE Number: 1294492
zbMATH Keywords: 16-dimensional compact projective planes
zbMATH Keywords: large groups of automorphisms
author: Helmut Salzmann
reviewed by: Markus Stroppel
MaRDI profile type: Publication
cites work: On the dimensions of automorphism groups of eight-dimensional ternary fields. II
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cites work: Compact 16-dimensional projective planes with large collineation groups
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cites work: Characterization of 16-dimensional Hughes planes
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description: scientific article; zbMATH DE number 1294492