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ELATION GENERALIZED QUADRANGLES FOR WHICH THE NUMBER OF LINES ON A POINT IS THE SUCCESSOR OF A PRIME

Part of: Finite geometry and special incidence structures

Published online by Cambridge University Press:  01 December 2008

JOHN BAMBERG ,
TIM PENTTILA  and
CSABA SCHNEIDER
JOHN BAMBERG*
Affiliation:
Department of Pure Mathematics, Ghent University, Galglaan 2, B-9000 Ghent, Belgium (email: bamberg@cage.ugent.be)
TIM PENTTILA
Affiliation:
Department of Mathematics, Colorado State University, Fort Collins, CO 80523, USA (email: penttila@math.colostate.edu)
CSABA SCHNEIDER
Affiliation:
Centro de Álgebra da Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal (email: csaba.schneider@gmail.com)
*
✉For correspondence; e-mail: bamberg@cage.ugent.be
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Abstract

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We show that an elation generalized quadrangle that has p+1 lines on each point, for some prime p, is classical or arises from a flock of a quadratic cone (that is, is a flock quadrangle).

Keywords

elation generalized quadrangleflockp-groupKantor family

MSC classification

Secondary: 51E12: Generalized quadrangles, generalized polygons
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 85 , Issue 3 , December 2008 , pp. 289 - 303
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

This research formed part of an Australian Research Council Discovery Grant project that was undertaken at the University of Western Australia. The first author was supported by a Marie Curie Incoming International Fellowship within the 6th European Community Framework Programme, contract number MIIF1-CT-2006-040360. The third author was supported by the Hungarian Scientific Research Fund (OTKA) grant F049040; he is also grateful to Hendrik Van Maldeghem for funding his visit to the workshop Groups and Buildings 2007 held in Ghent.

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