Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-25T06:48:37.106Z Has data issue: false hasContentIssue false
  • English
  • Français

COVERS OF GENERALIZED QUADRANGLES

Part of: Finite geometry and special incidence structures Linear incidence geometry Nonlinear incidence geometry Geometry Designs and configurations Algebraic combinatorics

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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 structures 51A10: Homomorphism, automorphism and dualities 51B25: Lie geometries 51E12: Generalized quadrangles, generalized polygons
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 3 , September 2018 , pp. 585 - 601
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

REFERENCES

1. Brown, M. R., Semipartial geometries and generalized quadrangles of order (r, r2), Finite geometry and combinatorics (Deinze, 1997), Bull. Belg. Math. Soc. Simon Stevin 5 (1998), 187–205.Google Scholar
2. Cardinali, I. and Sastry, N. S. N., Elliptic ovoids and their rosettes in a classical generalized quadrangle of even order, Proc. Indian Acad. Sci. Math. Sci. 126 (2016), 591–612.CrossRefGoogle Scholar
3. De Kaey, J. and Van Maldeghem, H., A characterization of the split Cayley generalized hexagon H(q) using one subhexagon of order (1, q), Discrete Math. 294 (2005), 109–118.Google Scholar
4. Hirschfeld, J. W. P. and Thas, J. A., General Galois geometries, 2nd edition, Springer Monographs in Mathematics (Springer, London, 2016).CrossRefGoogle Scholar
5. Payne, S. E. and Thas, J. A., Finite generalized quadrangles, 2nd edition, EMS Series of Lectures in Mathematics (European Mathematical Society (EMS), Zürich, 2009).Google Scholar
6. Thas, J. A., 3-regularity in generalized quadrangles: A survey, recent results and the solution of a longstanding conjecture, Combinatorics '98 (Mondello), Rend. Circ. Mat. Palermo (2) Suppl. No. 53 (1998), 199–218.Google Scholar
7. Thas, J. A., Thas, K. and Van Maldeghem, H., Translation generalized quadrangles, Series in Pure Mathematics, vol. 26 (World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2006).Google Scholar
8. Thas, K., Translation generalized quadrangles for which the translation dual arises from a flock, Glasg. Math. J. 45 (2003), 457–474.CrossRefGoogle Scholar
9. Thas, K., Symmetry in finite generalized quadrangles, Frontiers in Mathematics, vol. 1 (Birkhäuser Verlag, Basel, 2004).Google Scholar
10. Thas, K., A stabilizer lemma for translation generalized quadrangles, Eur. J. Combin. 28 (2007), 1–16.Google Scholar
11. Thas, K., A course on elation quadrangles, EMS Series of Lectures in Mathematics (European Mathematical Society (EMS), Zürich, 2012).Google Scholar
12. Thas, K. and Van Maldeghem, H., Geometric characterizations of finite Chevalley groups of type B 2, Trans. Amer. Math. Soc. 360 (2008), 2327–2357.Google Scholar
13. Van Maldeghem, H., Generalized polygons, Monographs in Mathematics, vol. 93 (Birkhäuser Verlag, Basel, 1998).Google Scholar