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Every generalized quadrangle of order 5 having a regular point is symplectic

Bart De Bruyn UGent (2015) EXPERIMENTAL MATHEMATICS. 24(1). p.45-52
abstract
For many years now, one of the most important open problems in the theory of generalized quadrangles has been whether other classes of generalized quadrangles exist besides those that are currently known. This paper reports on an unsuccessful attempt to construct a new generalized quadrangle. As a byproduct of our attempt, however, we obtain the following new characterization result: every generalized quadrangle of order 5 that has at least one regular point is isomorphic to the quadrangle W(5) arising from a symplectic polarity of PG(3, 5). During the classification process, we used the computer algebra system GAP to perform certain computations or to search for an optimal strategy for the proof.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
generalized quadrangle, regular point, (generalized) admissible triple, affine plane, COORDINATIZATION, SPREAD
journal title
EXPERIMENTAL MATHEMATICS
Exp. Math.
volume
24
issue
1
pages
45 - 52
Web of Science type
Article
Web of Science id
000349389100004
JCR category
MATHEMATICS
JCR impact factor
0.595 (2015)
JCR rank
167/312 (2015)
JCR quartile
3 (2015)
ISSN
1058-6458
DOI
10.1080/10586458.2014.952051
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
7140152
handle
http://hdl.handle.net/1854/LU-7140152
date created
2016-03-09 13:23:57
date last changed
2017-05-04 14:00:41
@article{7140152,
  abstract     = {For many years now, one of the most important open problems in the theory of generalized quadrangles has been whether other classes of generalized quadrangles exist besides those that are currently known. This paper reports on an unsuccessful attempt to construct a new generalized quadrangle. As a byproduct of our attempt, however, we obtain the following new characterization result: every generalized quadrangle of order 5 that has at least one regular point is isomorphic to the quadrangle W(5) arising from a symplectic polarity of PG(3, 5). During the classification process, we used the computer algebra system GAP to perform certain computations or to search for an optimal strategy for the proof.},
  author       = {De Bruyn, Bart},
  issn         = {1058-6458},
  journal      = {EXPERIMENTAL MATHEMATICS},
  keyword      = {generalized quadrangle,regular point,(generalized) admissible triple,affine plane,COORDINATIZATION,SPREAD},
  language     = {eng},
  number       = {1},
  pages        = {45--52},
  title        = {Every generalized quadrangle of order 5 having a regular point is symplectic},
  url          = {http://dx.doi.org/10.1080/10586458.2014.952051},
  volume       = {24},
  year         = {2015},
}

Chicago
De Bruyn, Bart. 2015. “Every Generalized Quadrangle of Order 5 Having a Regular Point Is Symplectic.” Experimental Mathematics 24 (1): 45–52.
APA
De Bruyn, B. (2015). Every generalized quadrangle of order 5 having a regular point is symplectic. EXPERIMENTAL MATHEMATICS, 24(1), 45–52.
Vancouver
1.
De Bruyn B. Every generalized quadrangle of order 5 having a regular point is symplectic. EXPERIMENTAL MATHEMATICS. 2015;24(1):45–52.
MLA
De Bruyn, Bart. “Every Generalized Quadrangle of Order 5 Having a Regular Point Is Symplectic.” EXPERIMENTAL MATHEMATICS 24.1 (2015): 45–52. Print.