The correlations of finite Desarguesian planes. I: Generalities
type: Item
instance of: scholarly article
title: The correlations of finite Desarguesian planes. I: Generalities
zbMATH Open document ID: 1029.51014
author: Barbu C. Kestenband
published in: Journal of Geometry
publication date: 2003-09-16T00:00:00Z
review text: This is a first paper in a sequence of papers which have as goal to classify the correlations in desarguesian projective planes. The classification of polarities is very well known and can be found in any textbook on this issue. For the correlations however, a lot of energy is needed to finish the job. The author announces in this paper that a complete classification of correlations of planes of odd nonsquare order is done; it will be treated in the forthcoming papers. The classification of correlations in planes of even nonsquare order as well as those in planes of square order are both projects the author is for the moment working on. In this first part the author presents general definitions and algebraic results that are needed in the subsequent parts. In order to lay the geometric groundwork for the actual classification the author establishes the equivalence classes of correlations, discusses certain general properties of correlations and introduces the concepts of residue class and character of an absolute point of a correlation, which will all play an important role in the classification.
Mathematics Subject Classification ID: 51E15
zbMATH DE Number: 1982545
zbMATH Keywords: correlation
zbMATH Keywords: desarguesian projective planes
MaRDI profile type: Publication
full work available at URL: s00022-003-1623-0
OpenAlex ID: W2083328404
DOI: 10.1007/S00022-003-1623-0
description: scientific article; zbMATH DE number 1982545