Research article

Results in Mathematics

, Volume 38, Issue 3, pp 270-306

First online:

Four-dimensional compact projective planes admitting an affine Hughes group

  • Hauke KleinAffiliated withMathematisches Seminar der Universität Email author 
  • , Norbert KnarrAffiliated withInstitut für Analysis der Technischen Universität Braunschweig
  • , Rainer LöwenAffiliated withInstitut für Analysis der Technischen Universität Braunschweig

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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

51H10 51A35 26B10

Key words

Compact projective plane Hughes group