Innovations in Incidence Geometry

Groups of hyperovals in Desarguesian planes

Luke Bayens, William Cherowitzo, and Tim Penttila

Full-text: Open access

Abstract

We show that if a hyperoval of PG ( 2 , q ) , q > 4 , admits an insoluble group G , then G fixes a subplane π 0 of order q 0 > 2 , meets π 0 in a regular hyperoval of π 0 on which G PGL ( 3 , q ) induces PGL ( 2 , q 0 ) , and if is not regular then q > q 0 2 . We also bound above the order of the homography stabilizer of a non-translation hyperoval of PG ( 2 , q ) by 3 ( q 1 ) . Finally, we show that the homography stabilizer of the Cherowitzo hyperovals is trivial for q > 8 .

Article information

Source
Innov. Incidence Geom., Volume 6-7, Number 1 (2007), 37-51.

Dates
Received: 1 March 2008
Accepted: 17 March 2008
First available in Project Euclid: 28 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.iig/1551323169

Digital Object Identifier
doi:10.2140/iig.2008.6.37

Mathematical Reviews number (MathSciNet)
MR2515257

Zentralblatt MATH identifier
1178.51006

Subjects
Primary: 51E20: Combinatorial structures in finite projective spaces [See also 05Bxx] 51E21: Blocking sets, ovals, k-arcs

Keywords
hyperoval group

Citation

Bayens, Luke; Cherowitzo, William; Penttila, Tim. Groups of hyperovals in Desarguesian planes. Innov. Incidence Geom. 6-7 (2007), no. 1, 37--51. doi:10.2140/iig.2008.6.37. https://projecteuclid.org/euclid.iig/1551323169


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