Innovations in Incidence Geometry

On polar ovals in cyclic projective planes

Kei Yuen Chan, Hiu Fai Law, and Philip P. W. Wong

Full-text: Open access

Abstract

A condition is introduced on the abelian difference set D of an abelian projective plane of odd order so that the oval 2 D is the set of absolute points of a polarity, with the consequence that any such abelian projective plane is Desarguesian.

Article information

Source
Innov. Incidence Geom., Volume 12, Number 1 (2011), 35-48.

Dates
Received: 15 December 2009
First available in Project Euclid: 28 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.iig/1551323067

Digital Object Identifier
doi:10.2140/iig.2011.12.35

Mathematical Reviews number (MathSciNet)
MR2942716

Zentralblatt MATH identifier
1302.51007

Subjects
Primary: 05B10: Difference sets (number-theoretic, group-theoretic, etc.) [See also 11B13] 05B25: Finite geometries [See also 51D20, 51Exx] 51E15: Affine and projective planes 51E21: Blocking sets, ovals, k-arcs

Keywords
ovals polarity cyclic difference sets projective planes

Citation

Chan, Kei Yuen; Law, Hiu Fai; Wong, Philip P. W. On polar ovals in cyclic projective planes. Innov. Incidence Geom. 12 (2011), no. 1, 35--48. doi:10.2140/iig.2011.12.35. https://projecteuclid.org/euclid.iig/1551323067


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