A new generalization of Moulton affine planes
type: Item
instance of: scholarly article
title: A new generalization of Moulton affine planes
zbMATH Open document ID: 0756.51007
DOI: 10.1007/BF02414064
author: Jan Jakóbowski
published in: Geometriae Dedicata
publication date: 1992-09-27T00:00:00Z
review text: Following \textit{W. A. Pierce} [Can. J. Math. 13, 427-436 (1961; Zbl 0103.134)], the author considers a variation on his construction of Moulton planes. However he takes a different view and describes lines of negative slope by equations \(g(y)=mf(x)+n\) and remaining lines by equations \(x=c\) or \(y=mx+n\) with \(m=0\). In Section 1 he investigates under what conditions on \(f\) and \(g\) we obtain an affine plane, in Section 2 he considers some special cases, including the case of finite fields. The questions are whether his construction really yields new planes not isomorphic to already known planes and under what conditions are the planes constructed in his article isomorphic to each other. At present the author does not know the answers but in Section 3 he describes some examples to give some idea of what is to be expected.
Mathematics Subject Classification ID: 51B20
zbMATH DE Number: 58792
zbMATH Keywords: generalization of Moulton affine spaces
reviewed by: Pavel Burda
MaRDI profile type: Publication
cites work: A Theorem on Permutations in a Finite Field
cites work: Q3676730
cites work: Moulton Planes
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description: scientific article; zbMATH DE number 58792