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Archiv der Mathematik

, Volume 73, Issue 1, pp 73–80 | Cite as

Smooth Hughes planes are classical

  • Richard Bödi
Article
  • 24 Downloads

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.

Keywords

Complex Number Projective Plane Collineation Group Classical Plane Compact Projective Plane 

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Copyright information

© Birkhäuser Verlag, Basel 1999

Authors and Affiliations

  • Richard Bödi
    • 1
  1. 1.Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, GermanyGermany

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