Innovations in Incidence Geometry

Collineation groups with one or two orbits on the set of points not on an oval and its nucleus

Gábor Korchmáros and Antonio Maschietti

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Projective planes of even order admitting a collineation group fixing an oval and having one or two orbits on the set of points not on the oval and its nucleus are investigated.

Article information

Innov. Incidence Geom., Volume 11, Number 1 (2010), 187-195.

Received: 4 November 2008
Accepted: 16 January 2009
First available in Project Euclid: 28 February 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 51A40: Translation planes and spreads 51E23: Spreads and packing problems

projective plane collineation group oval


Korchmáros, Gábor; Maschietti, Antonio. Collineation groups with one or two orbits on the set of points not on an oval and its nucleus. Innov. Incidence Geom. 11 (2010), no. 1, 187--195. doi:10.2140/iig.2010.11.187.

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  • M. Biliotti and G. Korchmáros, Collineation groups strongly irreducible on an oval, in Combinatorics '84 (Bari, 1984), pp. 85–97, North-Holland Math. Stud. 123, North-Holland, Amsterdam, 1986.
  • M. Biliotti, V. Jha and N. L. Johnson, Two-transitive parabolic ovals, J. Geom. 70 (2001), 17–27.
  • A. Bonisoli, On a theorem of Hering and two-transitive ovals with a fixed external line, in Mostly Finite Geometries (Iowa City, IA, 1996), pp. 169–183, Lect. Notes Pure Appl. Math. 190, Dekker, New York, 1997.
  • A. Bonisoli and G. Korchmáros, Irreducible collineation group fixing a hyperoval, J. Algebra 252 (2002), 431–448.
  • A. Delandtsheer and J. Doyen, A classification of line-transitive maximal $(v,k)$-arcs in finite projective planes, Arch. Math. 55 (1990), 187–192.
  • P. Dembowski, Finite Geometries, Ergeb. Math. Grenzgeb., Springer–Verlag, Berlin–Heidelberg–New York, 1968.
  • J. D. Dixon and B. Mortimer, Permutation Groups, Grad. Texts in Math. 163, Springer-Verlag, New York, 1996.
  • W. M. Kantor, $k$-homogeneous groups, Math. Z. 124 (1972), 261–265.
  • A. Maschietti, Two-transitive ovals, Adv. Geom. 6 (2006), 323–332.
  • ––––, Symplectic translation planes of even order, in Finite Geometries, Groups and Computation, pp. 125–140, Walter de Gruyter GmbH and Co. KG, Berlin, 2006.