On a class of derived translation planes of square order
type: Item
instance of: scholarly article
title: On a class of derived translation planes of square order
zbMATH Open document ID: 0673.51002
DOI: 10.1016/0024-3795(89)90399-6
author: M. L. Narayana Rao
author: G. Vithal Rao
author: K. Satyanarayana
published in: Linear Algebra and its Applications
publication date: 1989-01-01T00:00:00Z
review text: In earlier papers [Bull. Aust. Math. Soc. 30, 59--66 (1984; Zbl 0549.51002) and Discrete Math. 66, 175--190 (1987; Zbl 0621.51007)] the authors constructed a class of translation planes \(\pi\) of order \(q^2\), where \(q\) is an odd power of a prime such that 5 is a nonsquare in \(\mathrm{GF}(q)\). Now another class of translation planes \(\bar \pi\) is obtained from those planes \(\pi\) by derivation. In fact the planes \(\bar \pi\) turn out to be a class of planes which has been found by \textit{S. Cohen} and \textit{M. J. Ganley} [Q. J. Math. Oxf., II. Ser. 35, 101--113 (1984; Zbl 0541.51005)] by a different approach. A detailed description of the translation complements of the planes \(\bar \pi\) is given. This is used to establish that the classes of planes \(\pi\) and \(\bar \pi\) do not coincide.
Mathematics Subject Classification ID: 51A40
zbMATH DE Number: 4101972
zbMATH Keywords: translation planes
zbMATH Keywords: derivation
reviewed by: Hans Havlicek
MaRDI profile type: Publication
full work available at URL: 0024-3795(89)90399-6
OpenAlex ID: W2058824120
cites work: SOME CLASSES OF TRANSLATION PLANES
cites work: On Delta-transitive translation planes
cites work: Notes on the derived Walker planes
cites work: A class of translation planes of square order
cites work: On a class of translation planes of square order
description: scientific article; zbMATH DE number 4101972