A class of unitals of order q which can be embedded in two different planes of order \(q^ 2\)
type: Item
instance of: scholarly article
title: A class of unitals of order q which can be embedded in two different planes of order \(q^ 2\)
zbMATH Open document ID: 0623.51002
DOI: 10.1007/BF01234988
author: Klaus Grüning
published in: Journal of Geometry
publication date: 1987-01-01T00:00:00Z
review text: For every prime power \(q>2\) there exists a unital U of order q which is embeddable in two non-isomorphic projective planes of order \(q^ 2\), namely the Hall plane \(\Pi_ H(q^ 2)\) and its dual projective plane, respectively. The proof of this theorem is based upon the approach to construct translation planes of order \(q^ 2\) within PG(4,q) due to \textit{J. André} [Math. Z. 60, 156-186 (1954; Zbl 0056.385)] and a paper of \textit{F. Buekenhout} [Geom. Dedicaa 5, 189-194 (1976; Zbl 0336.50014)] on unitals in finite translation planes.
Mathematics Subject Classification ID: 51A45
Mathematics Subject Classification ID: 51A40
Mathematics Subject Classification ID: 51E30
zbMATH DE Number: 4011326
zbMATH Keywords: unitals embedded in projective plane
zbMATH Keywords: Hall plane
zbMATH Keywords: unitals in finite translation planes
reviewed by: Hans Havlicek
MaRDI profile type: Publication
cites work: Über nicht-Desarguessche Ebenen mit transitiver Translationsgruppe
cites work: Q3894556
cites work: Existence of unitals in finite translation planes of order \(q^2\) with a kernel of order \(q\)
cites work: Q5545191
cites work: Automorphisms of unitary block designs
cites work: Q5524221
full work available at URL: https://doi.org/10.1007/bf01234988
OpenAlex ID: W434424356
description: scientific article; zbMATH DE number 4011326