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Pseudo-Homogeneous Coordinates for Hughes Planes

Published online by Cambridge University Press:  20 November 2018

Peter Maier  and
Markus Stroppel
Peter Maier
Affiliation:
Fachbereich Mathematik der TH, Schlossgartenstr. 7, D-64289 Darmstadt
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Abstract

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Among the projective planes, the class of Hughes planes has received much interest, for several good reasons. However, the existing descriptions of these planes are somewhat unsatisfactory. We introduce pseudo-homogeneous coordinates which at the same time are easy to handle and give insight into the action of the group that is generated by all elations of the desarguesian Baer subplane of a Hughes plane. The information about the orbit decomposition is then used to give a description in terms of coset spaces of this group. Finally, we exhibit a non-closing Desargues configuration in terms of coordinates.

Keywords

Primary 51A35secondary 51A2551A10Hughes planesprojective planesspecial linear groupsnearfiledsorbit decompositions
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 3 , 01 September 1996 , pp. 330 - 345
Copyright
Copyright © Canadian Mathematical Society 1996

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