23 references, page 1 of 3 7.1 Corollary. Assume that P is not classical. If Δ is semi-simple and if dim Δ > 11 , then P is a Hughes plane or FΔ = {o, W } with o ∈/ W and dim Δ ≤ 13 .

This is a consequence of theorems 2.1, 3.1, 4.1, 4.4, 5.1, and 6.1.

9.3 Linearization. There exists an open neighbourhood U of p in P and a homeomorphism λ : U → TpP such that λ(L ∩ U ) = TpL for every line L ∈ Lp (cf. [6] 3.12).

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[3] D. Betten, On the classification of 4-dimensional flexible projective planes, Lect. Notes p. a. Math. 190 (1997), 9-33; R 98f: 51020

[4] R. B¨odi, On the dimensions of automorphism groups of four-dimensional double loops, Math. Z. 215 (1994), 89-97; R 95g: 22005

[5] R. B¨odi, Smooth stable and projective planes, Thesis, Tu¨bingen 1996; (www.mathematik.uni-tuebingen.de/ab/Geometrie.alt/Smoothstableplanes.ps)

[6] R. B¨odi, Smooth stable planes, Results Math. 31 (1997), 300-321; R 98e: 51021

[7] R. B¨odi, Collineations of smooth stable planes, Forum Math. 10 (1998), 751-773; R 99i: 51015