Abstract.
We prove that the only compact projective Hughes planes which are smooth projective planes are the classical planes over the complex numbers \(\Bbb C \), the quaternions \(\Bbb H \), and the Caley numbers \(\Bbb O \). As a by-product this shows that an 8-dimensional smooth projective plane which admits a collineation group of dimension \(d \geq 17\) is isomorphic to the quaternion projective plane \({\cal P _2\Bbb H }\). For topological compact projective planes this is true if \(d \geq 19\), and this bound is sharp.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 30.3.1998
Rights and permissions
About this article
Cite this article
Bödi, R. Smooth Hughes planes are classical. Arch. Math. 73, 73–80 (1999). https://doi.org/10.1007/s000130050022
Published:
Issue Date:
DOI: https://doi.org/10.1007/s000130050022