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COVERS OF GENERALIZED QUADRANGLES

Part of:Algebraic combinatoricsNonlinear incidence geometryFinite geometry and special incidence structuresLinear incidence geometryGeometryDesigns and configurations

Published online by Cambridge University Press:  25 January 2018

JOSEPH A. THAS and
KOEN THAS
JOSEPH A. THAS
Affiliation:
Department of Mathematics, Ghent University, Krijgslaan 281, S25, B-9000 Ghent, Belgium e-mails: thas.joseph@gmail.com, koen.thas@gmail.com
KOEN THAS
Affiliation:
Department of Mathematics, Ghent University, Krijgslaan 281, S25, B-9000 Ghent, Belgium e-mails: thas.joseph@gmail.com, koen.thas@gmail.com
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Abstract

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We solve a problem posed by Cardinali and Sastry (Elliptic ovoids and their rosettes in a classical generalized quadrangle of even order. Proc. Indian Acad. Sci. Math. Sci. 126 (2016), 591–612) about factorization of 2-covers of finite classical generalized quadrangles (GQs). To that end, we develop a general theory of cover factorization for GQs, and in particular, we study the isomorphism problem for such covers and associated geometries. As a byproduct, we obtain new results about semi-partial geometries coming from θ-covers, and consider related problems.

MSC classification

Primary:05B25: Finite geometries
Secondary:05E18: Group actions on combinatorial structures51A10: Homomorphism, automorphism and dualities51B25: Lie geometries51E12: Generalized quadrangles, generalized polygons

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 3 , September 2018, pp. 585 - 601
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

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