Generalized Quadrangles and Transitive Pseudo‐Hyperovals |
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| Authors: | John Bamberg S P Glasby Tomasz Popiel Cheryl E Praeger |
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| Affiliation: | 1. Centre for the Mathematics of Symmetry and Computation, School of Mathematics and Statistics, The University of Western Australia, Crawley, WA, Australia;2. Department of Mathematics, University of Canberra, Australia;3. King Abdulaziz University, Jeddah, Saudi Arabia |
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| 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). |
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| Keywords: | generalized quadrangle pseudo‐hyperoval primitive permutation group |
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