The correlations of finite Desarguesian planes, Part II: The classification (I)

This paper continues the classification of the correlations of planes of odd nonsquare order. Part I (Generalities) – see reference 1]-included introductory definitions and results (Section 1), algebraic preliminaries (Section 2), as well as a discussion of equivalent correlations (Section 3) and of their general properties (Section 4). The classification proper revolves around a special polynomial which can have one, two, or q + 1 zeros, or no zeros at all, and each of these four possibilities leads to different families of correlations. The present article contains Section 5, devoted to the cases in which the correlation is defined by a diagonal matrix (Subsection 5.1) or the polynomial in the preceding paragraph possesses q + 1 zeros (Subsection 5.2), one zero (Subsection 5.3) and two zeros (Subsection 5.4). Subsection 5.5 presents certain results to be used in the subsequent sections.