Suzuki groups, one-factorizations and Lüneberg planes
type: Item
instance of: scholarly article
title: Suzuki groups, one-factorizations and Lüneberg planes
zbMATH Open document ID: 0878.51001
DOI: 10.1016/0012-365X(95)00273-Y
published in: Discrete Mathematics
publication date: 1997-12-07T00:00:00Z
review text: All one-factorizations of the complete graph on \(q^2\), \(q=2^{2e+1}\), vertices admitting the one point stabilizer of the Suzuki group Sz\((q)\) as an automorphism group and having \(q-1\) prescribed one-factors are determined. These arise from the involutions in the group. Moreover, a method is described for studying translation planes of (even) order \(q^2\) admitting Sz\((q)\) as a collineation group fixing an oval and acting 2-transitively on its points. This method is based on the possibility to describe a projective plane with an oval by means of one-factorizations of certain complete graphs. Since the results obtained for the one-factorizations are suitable for computer calculations, the authors are able to give a characterization of the Lüneburg plane of order 64 (\(q=8\)).
Mathematics Subject Classification ID: 51A40
Mathematics Subject Classification ID: 51E21
Mathematics Subject Classification ID: 05C70
zbMATH DE Number: 1018469
zbMATH Keywords: Suzuki groups
zbMATH Keywords: one-factorizations
zbMATH Keywords: Lüneburg planes
Wikidata QID: Q114215602
author: A. Bonisoli
author: Gabor Korchmáros
reviewed by: Hubert Kiechle
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1018469