Generalized Quadrangles and Transitive Pseudo-Hyperovals

John Bamberg, Stephen GLASBY, Tomasz Popiel, Cheryl Praeger

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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 languageEnglish
Pages (from-to)151-164
Number of pages14
JournalJournal of Combinatorial Designs
Volume24
Issue number4
DOIs
Publication statusPublished - Mar 2016

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Hyperoval
Generalized Quadrangle
Flag-transitive
Normal subgroup
Projective Space
Automorphism Group
Deduce
Isomorphic
Subspace
Line

Cite this

Bamberg, John ; GLASBY, Stephen ; Popiel, Tomasz ; Praeger, Cheryl. / Generalized Quadrangles and Transitive Pseudo-Hyperovals. In: Journal of Combinatorial Designs. 2016 ; Vol. 24, No. 4. pp. 151-164.
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Bamberg, J, GLASBY, S, Popiel, T & Praeger, C 2016, 'Generalized Quadrangles and Transitive Pseudo-Hyperovals', Journal of Combinatorial Designs, vol. 24, no. 4, pp. 151-164. https://doi.org/10.1002/jcd.21411

Generalized Quadrangles and Transitive Pseudo-Hyperovals. / Bamberg, John; GLASBY, Stephen; Popiel, Tomasz; Praeger, Cheryl.

In: Journal of Combinatorial Designs, Vol. 24, No. 4, 03.2016, p. 151-164.

Research output: Contribution to journalArticle

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