A family of translation planes of order \(q^ 3\)
type: Item
instance of: scholarly article
title: A family of translation planes of order \(q^ 3\)
zbMATH Open document ID: 0764.51005
DOI: 10.1007/BF01225775
author: Chihiro Suetake
published in: Journal of Geometry
publication date: 1993-01-17T00:00:00Z
review text: Let \(q\) be an odd prime power such that \(q\notin\{3,7\}\). The author constructs translation planes of order \(q^ 3\) whose translation complement has an orbit of length \(q^ 3-1\) on the line at infinity. Considering additional orbit lengths occuring these planes are shown to be different from planes with the same property constructed by \textit{J. André} [Math. Z. 60, 156-186 (1954; Zbl 0056.385)], \textit{Y. Hiramine} [Osaka J. Math. 23, 563-575 (1986; Zbl 0609.51002)], and the author [Osaka J. Math. 22, 773-786 (1985; Zbl 0574.51005)].
reviewed by: Horst Szambien
Mathematics Subject Classification ID: 51A40
Mathematics Subject Classification ID: 51E15
Mathematics Subject Classification ID: 51E23
zbMATH DE Number: 98738
zbMATH Keywords: finite translation plane
zbMATH Keywords: spread
zbMATH Keywords: translation complement
MaRDI profile type: Publication
cites work: Über nicht-Desarguessche Ebenen mit transitiver Translationsgruppe
cites work: On translation planes of order \(q^ 3\) with an orbit of length \(q^ 3- 1\) on \(\ell _{\infty}\)
cites work: Q3891315
cites work: On quasifields
cites work: A new class of translation planes of order \(q^ 3\)
full work available at URL: https://doi.org/10.1007/bf01225775
OpenAlex ID: W2065257001
description: scientific article; zbMATH DE number 98738