A new class of translation planes of order \(q^ 3\)
type: Item
instance of: scholarly article
title: A new class of translation planes of order \(q^ 3\)
zbMATH Open document ID: 0574.51005
author: Chihiro Suetake
published in: Osaka Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: Using the Oyama's method [\textit{T. Oyama}, Osaka J. Math. 22, 35-54 (1985; Zbl 0561.51006)] the author is concerned with the problem of describing a new class of translation planes of order \(q^ 3\), where 2 is a non- square in GF(q). He shows that for \(q\neq 3\) the linear translation complement of any plane of this class is of order \(3(q-1)(q^ 3-1)\) and for \(q=3\) the plane is the Hering plane of order 27 [\textit{C. Hering}, Abh. Math. Semin. Univ. Hamb. 34, 203-208 (1970; Zbl 0195.502)], and the translation complement is isomorphic to SL(2,13). The paper concludes by showing that the planes differ from generalized André planes [\textit{J. André}, Math. Z. 60, 156-186 (1954; Zbl 0056.385)] and semifield planes.
reviewed by: K.Burian
Mathematics Subject Classification ID: 51A40
zbMATH DE Number: 3917106
zbMATH Keywords: translation planes
zbMATH Keywords: Hering plane
zbMATH Keywords: generalized André planes
zbMATH Keywords: semifield planes
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3917106