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  and the construction principle employing derived planes that was given by the second author . 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.