On the structure of the Figueroa unital and the existence of O'Nan configurations

Yee Ka Tai, Philip P.W. Wong
2014 Discrete Mathematics  
The finite Figueroa planes are non-Desarguesian projective planes of order q 3 for all prime powers q > 2, constructed algebraically in 1982 by Figueroa, and Hering and Schaeffer, and synthetically in 1986 by Grundhöfer. All Figueroa planes of finite square order are shown to possess a unitary polarity by de Resmini and Hamilton in 1998, and hence admit unitals. Hui and Wong (2012) have shown that these polar unitals do not satisfy a necessary condition, introduced by Wilbrink in 1983, for a
more » ... k in 1983, for a unital to be classical, and hence they are not classical. In this article we introduce and make use of a new alternative synthetic description of the Figueroa plane and unital to demonstrate the existence of O'Nan configurations, thus providing support to Piper's conjecture (1981).
doi:10.1016/j.disc.2014.04.012 fatcat:lrbbgizrbbdxxm575crgbhosem