Results in Mathematics

, Volume 38, Issue 3, pp 270–306

Four-dimensional compact projective planes admitting an affine Hughes group


    • Mathematisches Seminar der Universität
  • Norbert Knarr
    • Institut für Analysis der Technischen Universität Braunschweig
  • Rainer Löwen
    • Institut für Analysis der Technischen Universität Braunschweig
Research article

DOI: 10.1007/BF03322013

Cite this article as:
Klein, H., Knarr, N. & Löwen, R. Results. Math. (2000) 38: 270. doi:10.1007/BF03322013


By constructing all 4-dimensional affine Hughes planes that are not translation planes, we contribute the last missing part to the classification of all compact 4-dimensional projective planes having a non-solvable automorphism group of dimension at least 6. We use the information on the possible actions of the automorphism group obtained by the third author [5] and the construction principle employing derived planes that was given by the second author [4]. The unique solvabilty of certain nonlinear systems of equations has to be shown; this is done using topological degree techniques and delicate analytic arguments. Also the proof of continuity of the geometric operations is quite subtle.

Mathematics Subject Classification 2000


Key words

Compact projective planeHughes group

Copyright information

© Birkhäuser Verlag, Basel 2000