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Extra resources for 4-Dimensional compact projective planes with a 5-dimensional nilradical
In all cases we calculate f ' ( t ) = (y - (t + ½))2. This means that f'(t) = 0 can occur for only one t (y E ]R fixed) and this implies the strict monotonicity of f. It remains to check that f behaves correctly for Itl --+ o~. For t ~ oo the function f has the form f(t) = t3(3w+ - 4 z + ) + terms of lower order in t if 3w+ - 4z+ # 0 t(y 2 + ~1) + const. e. if (w+, z+) = ( - I , - ½ ) " For t ~ - c ~ one has similar expressions, replace the indices + by - . If 3w+ 4z+ # 0 then by the condition (R) this number is > 0.
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. 13. : Classification of solvable Lie algebras of sixth order with one nonnilpotent basis element, Izv.
Salzmann, H. : Kollineationsgruppen kompakter 4-dimensionaler Ebenen II, Math. Z. 121 (1971), 104-110. 18. Salzmann, H. : Elations in four-dimensional planes, TopologyAppL 3 (1973), 121-124. 19. Salzmann, H. : Compact Projective Planes, de Gmyter, Berlin, 1995.