Abstract

Nearfield models for $PG\left(2,q^2\right)$ and the Hughes plane of order $q^2$, based on the well-known field-theoretic model of $PG\left(2,q^2\right)$, are described. By way of the correspondences between these models, certain unitals, ovals, and a Baer subplane are easily described in the Hughes plane. Moreover, a partition of the Hughes plane into maximal $\left(q^2-q+1\right)$-arcs is presented.

Keywords

Mathematical Subject Classification 2000

Milestones

Authors