Vol. 2, No. 1, 2005

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

Roland D. Baker and Kenneth L. Wantz

Vol. 2 (2005), No. 1, 83–92
DOI: 10.2140/iig.2005.2.83
Abstract

Nearfield models for PG(2,q2) and the Hughes plane of order q2, based on the well-known field-theoretic model of PG(2,q2), 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 (q2 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