Generalized Quadrangles and Transitive Pseudo-Hyperovals

John Bamberg; Stephen Glasby; Tomasz Popiel; Cheryl Praeger

doi:10.1002/jcd.21411

Generalized Quadrangles and Transitive Pseudo-Hyperovals

John Bamberg, Stephen Glasby, Tomasz Popiel, Cheryl Praeger

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

308 Downloads (Pure)

Abstract

© 2014 Wiley Periodicals, Inc. A pseudo-hyperoval of a projective space, q even, is a set of subspaces of dimension such that any three span the whole space. We prove that a pseudo-hyperoval with an irreducible transitive stabilizer is elementary. We then deduce from this result a classification of the thick generalized quadrangles that admit a point-primitive, line-transitive automorphism group with a point-regular abelian normal subgroup. Specifically, we show that is flag-transitive and isomorphic to, where is either the regular hyperoval of PG(2, 4) or the Lunelli-Sce hyperoval of PG(2, 16).

Original language	English
Pages (from-to)	151-164
Number of pages	14
Journal	Journal of Combinatorial Designs
Volume	24
Issue number	4
DOIs	https://doi.org/10.1002/jcd.21411
Publication status	Published - 1 Apr 2016

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10.1002/jcd.21411

Bamberg et al., 2016 Generalized Quadrangles and Transitive Pseudo-Hyperovals
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Cite this

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title = "Generalized Quadrangles and Transitive Pseudo-Hyperovals",

abstract = "{\textcopyright} 2014 Wiley Periodicals, Inc. A pseudo-hyperoval of a projective space, q even, is a set of subspaces of dimension such that any three span the whole space. We prove that a pseudo-hyperoval with an irreducible transitive stabilizer is elementary. We then deduce from this result a classification of the thick generalized quadrangles that admit a point-primitive, line-transitive automorphism group with a point-regular abelian normal subgroup. Specifically, we show that is flag-transitive and isomorphic to, where is either the regular hyperoval of PG(2, 4) or the Lunelli-Sce hyperoval of PG(2, 16).",

author = "John Bamberg and Stephen Glasby and Tomasz Popiel and Cheryl Praeger",

year = "2016",

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doi = "10.1002/jcd.21411",

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T1 - Generalized Quadrangles and Transitive Pseudo-Hyperovals

AU - Bamberg, John

AU - Glasby, Stephen

AU - Popiel, Tomasz

AU - Praeger, Cheryl

PY - 2016/4/1

Y1 - 2016/4/1

N2 - © 2014 Wiley Periodicals, Inc. A pseudo-hyperoval of a projective space, q even, is a set of subspaces of dimension such that any three span the whole space. We prove that a pseudo-hyperoval with an irreducible transitive stabilizer is elementary. We then deduce from this result a classification of the thick generalized quadrangles that admit a point-primitive, line-transitive automorphism group with a point-regular abelian normal subgroup. Specifically, we show that is flag-transitive and isomorphic to, where is either the regular hyperoval of PG(2, 4) or the Lunelli-Sce hyperoval of PG(2, 16).

AB - © 2014 Wiley Periodicals, Inc. A pseudo-hyperoval of a projective space, q even, is a set of subspaces of dimension such that any three span the whole space. We prove that a pseudo-hyperoval with an irreducible transitive stabilizer is elementary. We then deduce from this result a classification of the thick generalized quadrangles that admit a point-primitive, line-transitive automorphism group with a point-regular abelian normal subgroup. Specifically, we show that is flag-transitive and isomorphic to, where is either the regular hyperoval of PG(2, 4) or the Lunelli-Sce hyperoval of PG(2, 16).

UR - http://arxiv.org/abs/1406.6445

U2 - 10.1002/jcd.21411

DO - 10.1002/jcd.21411

M3 - Article

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VL - 24

SP - 151

EP - 164

JO - Journal of Combinatorial Designs

JF - Journal of Combinatorial Designs

IS - 4

ER -

Generalized Quadrangles and Transitive Pseudo-Hyperovals

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Finite linearly representable geometries and symmetry

Permutation Groups & their Interrelationship with the Symmetry of Graphs Codes & Geometric Configurations

Finite geometry from an algebraic point of view

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Generalized Quadrangles and Transitive Pseudo-Hyperovals

Abstract

Access to Document

Other files and links

Fingerprint

Projects

Finite linearly representable geometries and symmetry

Permutation Groups & their Interrelationship with the Symmetry of Graphs Codes & Geometric Configurations

Finite geometry from an algebraic point of view

Cite this