Semifield planes of order 81
type: Item
instance of: scholarly article
title: Semifield planes of order 81
zbMATH Open document ID: 1175.12003
author: Ulrich Dempwolff
published in: Journal of Geometry
publication date: 2009-06-08T00:00:00Z
review text: The semifield planes of dimension \(2\) over their left nucleus and dimension \(4\) over their center have been completely classified by \textit{I. Cardinali, O. Polverino} and \textit{R. Trombetti} [Eur. J. Comb. 27, No. 6, 940--961 (2006; Zbl 1108.51010)]. This implies that the planes of dimension \(2\) over one of their nuclei and dimension \(4\) over their center are all known. Therefore, if the semifield plane has order \(81,\) it was still open the case all nuclei are \(\text{GF}(3)\). In this paper the author gives a complete enumeration of such planes proving that some of them are not previously known. The enumeration has been done with a computer and the comprehensive files in GAP-format can by obtained from the homepage of the author.
reviewed by: Guglielmo Lunardon
Mathematics Subject Classification ID: 12K10
Mathematics Subject Classification ID: 51A40
zbMATH DE Number: 5562592
zbMATH Keywords: finite semifields
zbMATH Keywords: computer enumeration
MaRDI profile type: Publication
full work available at URL: s00022-008-1995-2
OpenAlex ID: W2160266619
DOI: 10.1007/S00022-008-1995-2
description: scientific article; zbMATH DE number 5562592