Notes on elation generalized quadrangles |
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Authors: | Stanley E. Payne Koen Thas |
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Affiliation: | a Department of Mathematics, University of Colorado at Denver, Campus Box 170, P.O. Box 173364, Denver, CO 80217-3364, USA;b Department of Pure Mathematics and Computer Algebra, Ghent University, Galglaan 2, B-9000, Ghent, Belgium |
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Abstract: | Let be a finite generalized quadrangle of order (s,t),s,t>1. An “elation about a point p” of is an automorphism fixing p linewise and fixing no point which is not collinear with p. An elation that generates a cyclic group of elations is called a “standard elation”. One of the problems already considered in Payne and Thas (Finite Generalized Quadrangles (1984)) is to determine just when the set of elations about the point (∞) is a group. The purpose of this paper is to provide an example where this is not the case, and then to show that for a flock generalized quadrangle the usual group of elations about (∞) is the complete set of standard elations about (∞). |
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Keywords: | Generalized quadrangle Elation Flock generalized quadrangle |
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