Images of conics under derivation Original Research Article

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 nondashdegenerate 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.