Abstract
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.
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Klein, H., Knarr, N. & Löwen, R. Four-dimensional compact projective planes admitting an affine Hughes group. Results. Math. 38, 270–306 (2000). https://doi.org/10.1007/BF03322013
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DOI: https://doi.org/10.1007/BF03322013