Bulletin of the Belgian Mathematical Society - Simon Stevin

Some Basic Questions and Conjectures on Elation Generalized Quadrangles, and their Solutions

Koen Thas

Full-text: Open access

Abstract

In this paper, I will start with posing three fundamental and old questions on (elation) generalized quadrangles, and survey tersely answers on these questions coming from recent work of S. E. Payne and the author of this paper. I will then introduce a fourth question posed recently by S. E. Payne, and will provide a general answer to this question, a result independently obtained by R. Rostermundt for the Hermitian quadrangles $H(3,q^2)$, $q$ even, in an entirely different fashion. Finally, I will show that this answer yields examples of elation generalized quadrangles for which the automorphism group fixing the elation point is not induced by the automorphisms of the elation group fixing the associated $4$-gonal family.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 12, Number 5 (2006), 909-918.

Dates
First available in Project Euclid: 10 January 2006

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1136902625

Mathematical Reviews number (MathSciNet)
MR2241353

Zentralblatt MATH identifier
1139.51010

Citation

Thas , Koen. Some Basic Questions and Conjectures on Elation Generalized Quadrangles, and their Solutions. Bull. Belg. Math. Soc. Simon Stevin 12 (2006), no. 5, 909--918. https://projecteuclid.org/euclid.bbms/1136902625


Export citation