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Additional info for 4-Dimensional compact projective planes with a 5-dimensional nilradical
7. : Homologies and elations in compact, connected projective planes, TopologyAppL 12 (1981), 49-63. 8. : Topologische Differenzenfltichenebenen, Kiel, 1983. 9. Knarr, N. : Ein Kriterium fiir topologische Tem~rk6rper, Arch. Math. 46 (1986), 368-370. 10. 2, Results Math. 12 (1987), 134-147. 11. :4-dimensionaleprojektiveEbenenmitgrol]erabelscherKollineationsgmppe, J. Geom. 31 (1988), 114-124. 12. : Four-dimensional compact projective planes with a nonsolvable automorphism group, Geom. Dedicata 36 (1990), 225-234.
This leads to the following system of equations: w~(x+t)(x + t) 3 - w~(z)x 3 - ty + bx = m We have to show that for m, n C ~ and (t, b) # (0, 0) there exists a solution (x, y) C I~ 2. Since this is obvious for t = 0 we may suppose t # 0. Eliminating y we get one equation for z. e. if (w+, z+) = (~, ~4). 4-DIMENSIONALCOMPACTPROJECTIVEPLANESWITH A 5-DIMENSIONALNILRADICAL 289 F o r x ~ - oo w e get similar expressions, replace the indices + b y - . F r o m (R) and (L) it f o l l o w s that 4 z + - w + _< 0 and 4 z _ - w _ _< 0.
9. Knarr, N. : Ein Kriterium fiir topologische Tem~rk6rper, Arch. Math. 46 (1986), 368-370. 10. 2, Results Math. 12 (1987), 134-147. 11. :4-dimensionaleprojektiveEbenenmitgrol]erabelscherKollineationsgmppe, J. Geom. 31 (1988), 114-124. 12. : Four-dimensional compact projective planes with a nonsolvable automorphism group, Geom. Dedicata 36 (1990), 225-234. 13. : Classification of solvable Lie algebras of sixth order with one nonnilpotent basis element, Izv. Vyssh. Uchebn. Zaved. Matematica 4 (1963), 104-116.