Maximal Baer groups in translation planes and compatibility with homology groups
type: Item
instance of: scholarly article
title: Maximal Baer groups in translation planes and compatibility with homology groups
zbMATH Open document ID: 0847.51003
DOI: 10.1007/BF00181527
author: Mauro Biliotti
author: Norman L. Johnson
published in: Geometriae Dedicata
publication date: 1996-10-20T00:00:00Z
review text: The authors determine all translation planes of order \(q^2\) and kernel containing \(GF(q)\) which admit at least two Baer groups of order \(q - 1\) in the translation complement: Such a plane \(\pi\) is in general a Hall plane. There are, however, some exceptional cases for \(q = 3,4,5\): the Desarguesian plane of order 9, the semifield plane of order 16 with kernel \(GF(4)\), the irregular nearfield plane of order 25, the exceptional Walker plane of order 25 with orbit structure 10, 16 on the line at infinity. Moreover, due to a result by one of the authors [\textit{N. L. Johnson}, Simon Stevin 63, No. 2, 167-188 (1989; Zbl 0702.51006)] the results are transferred to partial hyperbolic flocks: thus some new examples of maximal partial hyperbolic flocks in \(PG(3,5)\) are constructed.
reviewed by: Hans Havlicek
Mathematics Subject Classification ID: 51A40
Mathematics Subject Classification ID: 51E23
zbMATH DE Number: 843603
zbMATH Keywords: translation plane
zbMATH Keywords: Bear groups
zbMATH Keywords: hyperbolic flocks
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00181527
OpenAlex ID: W1979707626
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description: scientific article; zbMATH DE number 843603