Inherited unitals in Moulton planes

Authors

  • Gábor Korchmáros Dipartimento di Matematica, Informatica ed Economia Università degli Studi della Basilicata Viale dell'Ateneo Lucano 10, 85100 Potenza, Italy
  • Angelo Sonnino Dipartimento di Matematica, Informatica ed Economia Università degli Studi della Basilicata Viale dell'Ateneo Lucano 10, 85100 Potenza, Italy
  • Tamás Szőnyi Institute of Mathematics and MTA-ELTE GAC Research Group Eötvös Loránd University 1117 Budapest, Pázmány Péter s. 1/C, Ungary

DOI:

https://doi.org/10.26493/1855-3974.1285.f3c

Keywords:

Unitals, Moulton planes

Abstract

We prove that every Moulton plane of odd order—by duality every generalised André plane—contains a unital. We conjecture that such unitals are non-classical, that is, they are not isomorphic, as designs, to the Hermitian unital. We prove our conjecture for Moulton planes which differ from PG(2, q2) by a relatively small number of point-line incidences. Up to duality, our results extend previous analogous results—due to Barwick and Grüning—concerning inherited unitals in Hall planes.

Published

2017-09-04

Issue

Section

Articles