An arc partition of the Hughes plane using a field-theoretic model

Nearfield models for $PG (2, q^{2})$ and the Hughes plane of order $q^{2}$ , based on the well-known field-theoretic model of $PG (2, q^{2})$ , 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 $(q^{2} - q + 1)$ -arcs is presented.

Keywords

nearfield, arc partition, Hughes plane

Mathematical Subject Classification 2000

Primary: 51E20, 51E21

Milestones

Received: 7 February 2005

Accepted: 31 August 2005

Authors

Roland D. Baker


Kenneth L. Wantz

Vol. 2, No. 1, 2005

Roland D. Baker and Kenneth L. Wantz

Abstract

Keywords

Mathematical Subject Classification 2000

Milestones

Authors