COVERS OF GENERALIZED QUADRANGLES
Glasgow mathematical journal, Tome 60 (2018) no. 3, pp. 585-601

Voir la notice de l'article provenant de la source Cambridge University Press

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.
THAS, JOSEPH A.; THAS, KOEN. COVERS OF GENERALIZED QUADRANGLES. Glasgow mathematical journal, Tome 60 (2018) no. 3, pp. 585-601. doi: 10.1017/S0017089517000313
@article{10_1017_S0017089517000313,
     author = {THAS, JOSEPH A. and THAS, KOEN},
     title = {COVERS {OF} {GENERALIZED} {QUADRANGLES}},
     journal = {Glasgow mathematical journal},
     pages = {585--601},
     year = {2018},
     volume = {60},
     number = {3},
     doi = {10.1017/S0017089517000313},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089517000313/}
}
TY  - JOUR
AU  - THAS, JOSEPH A.
AU  - THAS, KOEN
TI  - COVERS OF GENERALIZED QUADRANGLES
JO  - Glasgow mathematical journal
PY  - 2018
SP  - 585
EP  - 601
VL  - 60
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089517000313/
DO  - 10.1017/S0017089517000313
ID  - 10_1017_S0017089517000313
ER  - 
%0 Journal Article
%A THAS, JOSEPH A.
%A THAS, KOEN
%T COVERS OF GENERALIZED QUADRANGLES
%J Glasgow mathematical journal
%D 2018
%P 585-601
%V 60
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089517000313/
%R 10.1017/S0017089517000313
%F 10_1017_S0017089517000313

[1] 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] 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. Google Scholar | DOI

[3] 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] 4. Hirschfeld, J. W. P. and Thas, J. A., General Galois geometries, 2nd edition, Springer Monographs in Mathematics (Springer, London, 2016). Google Scholar | DOI

[5] 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] 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] 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] 8. Thas, K., Translation generalized quadrangles for which the translation dual arises from a flock, Glasg. Math. J. 45 (2003), 457–474. Google Scholar | DOI

[9] 9. Thas, K., Symmetry in finite generalized quadrangles, Frontiers in Mathematics, vol. 1 (Birkhäuser Verlag, Basel, 2004). Google Scholar

[10] 10. Thas, K., A stabilizer lemma for translation generalized quadrangles, Eur. J. Combin. 28 (2007), 1–16. Google Scholar

[11] 11. Thas, K., A course on elation quadrangles, EMS Series of Lectures in Mathematics (European Mathematical Society (EMS), Zürich, 2012). Google Scholar

[12] 12. Thas, K. and Van Maldeghem, H., Geometric characterizations of finite Chevalley groups of type B , Trans. Amer. Math. Soc. 360 (2008), 2327–2357. Google Scholar

[13] 13. Van Maldeghem, H., Generalized polygons, Monographs in Mathematics, vol. 93 (Birkhäuser Verlag, Basel, 1998). Google Scholar

Cité par Sources :