Images of conics under derivation

✍ Scribed by Christine M. O'Keefe; Arlene A. Pascasio

• Book ID: 103059853
• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 617 KB
• Volume: 151
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(94)00096-2

✦ Synopsis

The Hall plane of order q2 is constructed from the Desarguesian plane of order q2 by the process of derivation with respect to a fixed derivation set on a fixed ideal line. The affine points of a non-degenerate conic in the Desarguesian plane of order q2 can be regarded as a set of points in the corresponding Hall plane.

We give a classification of the structure of sets of points in Hall planes arising from conics with two points in the derivation set. Further, if q is even, we classify the sets of points in Hall planes arising from conics which admit the ideal line as a tangent and are such that either the point of contact or the nucleus of the conic (or both) is contained in the derivation set.