Eine Charakterisierung der Lüneburgebenen
type: Item
instance of: scholarly article
title: Eine Charakterisierung der Lüneburgebenen
zbMATH Open document ID: 0569.51004
DOI: 10.1007/BF02941435
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1984-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 51A40
zbMATH DE Number: 3909209
zbMATH Keywords: characterizations of translation planes by groups
zbMATH Keywords: characterizations of Lüneburg planes
zbMATH Keywords: Suzuki group
author: Wolfram Buettner
reviewed by: Guangyu Shen
MaRDI profile type: Publication
cites work: A NEW TYPE OF SIMPLE GROUPS OF FINITE ORDER
cites work: Suzuki 2-groups
full work available at URL: https://doi.org/10.1007/bf02941435
OpenAlex ID: W2331737460
description: scientific article; zbMATH DE number 3909209