Generalized Quadrangles and the Moufang Condition

Hendrik Van Maldeghem (Ghent)

The Moufang condition for generalized quadrangles (or, more generally, for polygons) characterizes the examples arising from (simple) algebraic groups, classical groups and groups of so-called mixed type. We will present several conditions, which are logically weaker, but turn out to be equivalent to the Moufang condition. Amongst them the generalization to the infinite case of a condition used by Fong and Seitz in 1974 to characterize finite Chevalley groups of rank 2 (and a new proof of that result emerges).

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