The correlations of finite Desarguesian planes. I: Generalities
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.
scientific article; zbMATH DE number 1982545