Subplanes of order 3 in Figueroa planes
type: Item
instance of: scholarly article
title: Subplanes of order 3 in Figueroa planes
zbMATH Open document ID: 1272.51002
author: Cafer Caliskan
author: Bryan Petrak
published in: Finite Fields and their Applications
publication date: 2013-03-20T00:00:00Z
review text: The authors consider the problem concerning non--Desarguesian planes and their subplane structures on which little is still known. In particular, they consider the case of Figueroa planes of order \(q^3\). The second author showed in [J. Geom. 99, No. 1--2, 101--106 (2010; Zbl 1231.51007)] that Fano subplanes exist in Figueroa planes of order \(q^3\), \(q\) any prime power. In this paper, the case of subplanes of order \(3\) in Figueroa planes of order \(q^3\) is considered and the following theorem is proved. Theorem. Every Figueroa plane of order \(q^3\), where \(q\) is an odd prime power, has a subplane of order \(3\).
reviewed by: V. Napolitano
Mathematics Subject Classification ID: 51E15
zbMATH DE Number: 6146993
zbMATH Keywords: projective plane
zbMATH Keywords: subplane
MaRDI profile type: Publication
full work available at URL: j.ffa.2012.11.003
OpenAlex ID: W2090339309
DOI: 10.1016/J.FFA.2012.11.003
description: scientific article; zbMATH DE number 6146993