TY - JOUR
T1 - Generalized Quadrangles and Transitive Pseudo-Hyperovals
AU - Bamberg, John
AU - GLASBY, Stephen
AU - Popiel, Tomasz
AU - Praeger, Cheryl
PY - 2016/3
Y1 - 2016/3
N2 - 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 - 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).
KW - generalized quadrangle
KW - primitive permutation group
KW - pseudo-hyperoval
UR - http://www.scopus.com/inward/record.url?scp=84958120348&partnerID=8YFLogxK
UR - http://www.mendeley.com/research/generalized-quadrangles-transitive-pseudohyperovals
U2 - 10.1002/jcd.21411
DO - 10.1002/jcd.21411
M3 - Article
SN - 1063-8539
VL - 24
SP - 151
EP - 164
JO - Journal of Combinatorial Designs
JF - Journal of Combinatorial Designs
IS - 4
ER -