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Publication type: Article in scientific journal
Type of review: Peer review (publication)
Title: Smooth Hughes planes are classical
Authors: Bödi, Richard
DOI: 10.21256/zhaw-1735
Published in: Archiv der Mathematics
Volume(Issue): 73
Issue: 1
Page(s): 73
Pages to: 80
Issue Date: Jul-1999
Publisher / Ed. Institution: Springer
Publisher / Ed. Institution: Basel
ISSN: 0003-889X
Language: English
Subjects: Complex number; Projective plane; Collineation group; Classical plane; Compact projective plane
Subject (DDC): 510: Mathematics
Abstract: We prove that the only compact projective Hughes planes which are smooth projective planes are the classical planes over the complex numbers C, the quaternions H, and the Caley numbers O. As a by-product this shows that an 8-dimensional smooth projective plane which admits a collineation group of dimension d≥17 is isomorphic to the quaternion projective plane P 2 H. For topological compact projective planes this is true if d≥19, and this bound is sharp.
Further description: Erworben im Rahmen der Schweizer Nationallizenzen (
Fulltext version: Published version
License (according to publishing contract): Licence according to publishing contract
Departement: School of Engineering
Appears in collections:Publikationen School of Engineering

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Bödi, R. (1999). Smooth Hughes planes are classical. Archiv Der Mathematics, 73(1), 73–80.
Bödi, R. (1999) ‘Smooth Hughes planes are classical’, Archiv der Mathematics, 73(1), pp. 73–80. Available at:
R. Bödi, “Smooth Hughes planes are classical,” Archiv der Mathematics, vol. 73, no. 1, pp. 73–80, Jul. 1999, doi: 10.21256/zhaw-1735.
BÖDI, Richard, 1999. Smooth Hughes planes are classical. Archiv der Mathematics. Juli 1999. Bd. 73, Nr. 1, S. 73–80. DOI 10.21256/zhaw-1735
Bödi, Richard. 1999. “Smooth Hughes Planes Are Classical.” Archiv Der Mathematics 73 (1): 73–80.
Bödi, Richard. “Smooth Hughes Planes Are Classical.” Archiv Der Mathematics, vol. 73, no. 1, July 1999, pp. 73–80,

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