On Möbius spaces admitting automorphism groups of type II.2
type: Item
instance of: scholarly article
title: On Möbius spaces admitting automorphism groups of type II.2
zbMATH Open document ID: 1221.51017
author: Hans-Joachim Kroll
author: Sayed-Ghahreman Taherian
published in: Results in Mathematics
publication date: 2011-06-22T00:00:00Z
review text: The authors study Möbius spaces admitting an automorphism group of type II.2. Let \(\mathcal{O}\) denote an ovoid in the projective space \((\mathfrak{P},\mathfrak{G})\) of dimension at least \(3\), and let \((\mathcal{O},\mathfrak{K})\) denote the geometry of plane sections of \(\mathcal{O}\). Further let \(\Gamma < \text{Aut}(\mathcal{O},\mathfrak{K})\) be a subgroup of type II.2, then the set \(S=S_\Gamma\) is an \(\infty\)-maximal subspace of \((\mathcal{O},\mathfrak{K})\). The main result is the following: If \(S\) contains a hypersphere, then either the Möbius space \((\mathcal{O},\mathfrak{K})\) is miquelian, or char\,\(K = 2\) and \((\mathcal{O},\mathfrak{K})\) is of type III.2. For the case char \(K = 2\), more detailed results are provided.
Mathematics Subject Classification ID: 51F15
Mathematics Subject Classification ID: 20N05
zbMATH DE Number: 5911449
zbMATH Keywords: Möbius space
zbMATH Keywords: Möbius plane
zbMATH Keywords: Hering classification
reviewed by: Erich W. Ellers
MaRDI profile type: Publication
full work available at URL: s00025-011-0099-8
OpenAlex ID: W2059308023
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DOI: 10.1007/S00025-011-0099-8
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description: scientific article; zbMATH DE number 5911449