Generalized Quadrangles with Distinct Translation Points

2006 ◽  
pp. 109-114
Keyword(s):  
Generalized Quadrangles

scholarly journals MOUFANG QUADRANGLES OF MIXED TYPE

2008 ◽  
Vol 50 (1) ◽  
pp. 143-161
Author(s):  
KOEN STRUYVE ◽  
HENDRIK VAN MALDEGHEM
Keyword(s):  
Mixed Type ◽  
Geometric Characterization ◽  
Weak Version ◽  
Generalized Quadrangles

AbstractIn this paper, we present some geometric characterizations of the Moufang quadrangles of mixed type, i.e., the Moufang quadrangles all the points and lines of which are regular. Roughly, we classify generalized quadrangles with enough (to be made precise) regular points and lines with the property that the dual nets associated to the regular points satisfy the Axiom of Veblen-Young, or a very weak version of the Axiom of Desargues. As an application we obtain a geometric characterization and axiomatization of the generalized inversive planes arising from the Suzuki-Tits ovoids related to a polarity in a mixed quadrangle. In the perfect case this gives rise to a characterization with one axiom less than in a previous result by the second author.

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