THE CORRELATIONS OF FINITE DESARGUESIAN PLANES OF EVEN NONSQUARE ORDER

Barbu C. Kestenband (USA)

Abstract

The present article continues the classification of correlations of finite Desarguesian planes. In [Linear Algebra Appl. 304 (2000), 1-31] we have presented the correlations with identity companion automorphism which are not polarities, of these planes. Then, in [J. Geom. 77 (2003), 61-101], [B. C. Kestenband, The correlations of finite Desarguesian planes, Part II: The classification (I), J. Geom. (to appear)], [B. C. Kestenband, The correlations of finite Desarguesian planes, Part III: The classification (II), J. Geom. (to appear)], [B. C. Kestenband, The correlations of finite Desarguesian planes, Part IV: The classification (III), J. Geom. (to appear)], we classified the correlations of planes of order with companion automorphism an odd prime, t ¹ 0. In this paper we discuss the situation in which p = 2. This represents a complete classification of the correlations of planes of even nonsquare order (i = 0). Some of the correlations of planes of even square order (i ¹ 0) are also covered by the present analysis.

Keywords and phrases: correlation, absolute point (AP), absolute set, companion automorphism, q^m -equivalence, character of an absolute point, proper absolute point, arc of proper character.