Innovations in Incidence Geometry

Derivable subregular planes

Norman L. Johnson

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The set of subregular translation planes admitting a derivable net that lies across the subregular plane and the associated Desarguesian plane is completely classified as the set of Foulser-Ostrom planes of odd order.

Article information

Innov. Incidence Geom., Volume 3, Number 1 (2006), 89-108.

Received: 14 March 2006
First available in Project Euclid: 28 February 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

subregular planes derivable nets


Johnson, Norman L. Derivable subregular planes. Innov. Incidence Geom. 3 (2006), no. 1, 89--108. doi:10.2140/iig.2006.3.89.

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  • M. Biliotti, V. Jha and N. L. Johnson, Foundations of Translation Planes, Monographs and Textbooks in Pure and Applied Mathematics, vol. 243, Marcel Dekker Inc., New York, 2001.
  • D. A. Foulser, Derived translation planes admitting affine elations, Math. Z. 131 (1973), 183–188.
  • ––––, A translation plane admitting Baer collineations of order $p$, Arch. Math. (Basel) 24 (1973), 323–326.
  • V. Jha and N. L. Johnson, The Foulser-Ostrom planes, Journal of Geometry and Topology (to appear).
  • N. L. Johnson, Lezioni sui Piani di Traslazione, Quaderni del Departimento di Matematica dell'Università di Lecce, Q. 3, 1986 (Italian).
  • ––––, Subplane Covered Nets, Monographs and Textbooks in Pure and Applied Mathematics, vol. 222, Marcel Dekker Inc., New York, 2000.
  • ––––, Homology groups of translation planes and flocks of quadratic cones, I: The structure, Bull. Belg. Math. Soc. Simon Stevin 12 (2006), no. 5, 827–844.
  • W. F. Orr, A characterization of subregular spreads in finite $3$-space, Geom. Dedicata 5 (1976), no. 1, 43–50.
  • T. G. Ostrom, A class of translation planes admitting elations which are not translations, Arch. Math. (Basel) 21 (1970), 214–217.
  • J. A. Thas, Flocks of finite egglike inversive planes, Finite Geometric Structures and Their Applications (C.I.M.E., II Ciclo, Bressanone, 1972), Edizioni Cremonese, Rome, 1973, pp. 189–191.