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Local Sharply Transitive Actions on Finite Generalized Quadrangles
Theo Grundhöfer1 and Hendrik Van Maldeghem2
1Institut f¨ur Mathematik, Universit¨at W¨urzburg, Am Hubland, D-97074 Würzburg, Germany
grundh@mathematik.uni-wuerzburg.de
2Department for Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281,
S22, B-9000 Gent, Belgium
hvm@cage.UGent.be
Annals of Combinatorics 15 (1) pp.69-80 January, 2011
AMS Subject Classification: 51E12
Abstract:
We classify the finite generalized quadrangles containing a line L such that some group of collineations acts sharply transitively on the ordered pentagons which start with two points of L. This can be seen as a generalization of a result of Thas and the second author [22] classifying all finite generalized quadrangles admitting a collineation group that acts transitively on all ordered pentagons, although the restriction to sharp transitivity is essential in our arguments. However, the conclusion is exactly the same family of classical generalized quadrangles (the orthogonal quadrangles and their duals). Our main result thus provides a local group theoretic characterization of these classical quadrangles.
Keywords: Moufang panel, root elations, classical generalized quadrangles

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