By Betten D.

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E. w+ = ~ , z + = , or w_ = ,z_ = , or both. 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 - .

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. 14. Ortega, J. M. and Rheinboldt, W. : lterative Solution of Nonlinear Equations in Several Variables, Academic Press New York: (1970). 15. Salzmann, H. : Topological planes, Adv. Math. 2, (1967), 1-60.

Uchebn. Zaved. Matematica 4 (1963), 104-116. 14. Ortega, J. M. and Rheinboldt, W. : lterative Solution of Nonlinear Equations in Several Variables, Academic Press New York: (1970). 15. Salzmann, H. : Topological planes, Adv. Math. 2, (1967), 1-60. 16. Salzmann, H. : Kollineationsgmppen kompakter vier-dimensionaler Ebenen, Math. Z. 117 (1970), 112-124. 17. 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.

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4-Dimensional compact projective planes with a 5-dimensional nilradical by Betten D.


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