Eine Charakterisierung der Lüneburgebenen
Let G be a group of automorphisms of the translation plane (V,N) where V is a vector space and N is a spread in V. G is said to characterize (V,N) if every imbedding of G in \(\Gamma\) L(V) (the group of semilinear transformations of V) fixes a spread \(N^ 1\) in V such that \((V,N^ 1)\) is isomorphic to (V,N). It is known [\textit{H. Lüneburg}, Die Suzukigruppen und ihre Geometrien, Lect. Notes Math. 10 (1965; Zbl 0136.015)] that the Lüneburg plane of order \(q^ 2\) is characterized by the Suzuki group Sz(q). It is shown that the normalizer of a Sylow 2-group of Sz(q) characterizes the Lüneburg plane, and every proper subgroup of Sz(q) that characterizes the Lüneburg plane is contained in such a normalizer.
characterizations of translation planes by groups
scientific article; zbMATH DE number 3909209