Moufang sets related to polarities in exceptional Moufang quadrangles of type F 4

Moufang quadrangles: A unifying algebraic structure, and some results on exceptional quadrangles

Moufang Quadrangles of Mixed type

In 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 net associated to the regular points satisfy the Axiom of Veblen-Young, or a very we...

Quadrangles embedded in metasymplectic spaces

During the final steps in the classification of the Moufang quadrangles by Jacques Tits and Richard Weiss a new class of Moufang quadrangles unexpectedly turned up. Subsequently Bernhard Mühlherr and Hendrik Van Maldeghem showed that this class arises as the fixed points and hyperlines of certain involutions of a metasymplectic space (or equivalently a building of type F4). In the same paper th...

Geometric Characterizations of Finite Chevalley Groups of Type B2

Finite Moufang generalized quadrangles were classified in 1974 as a corollary to the classification of finite groups with a split BN-pair of rank 2, by P. Fong and G. M. Seitz (1973), (1974). Later on, work of S. E. Payne and J. A. Thas culminated in an almost complete, elementary proof of that classification; see Finite Generalized Quadrangles, 1984. Using slightly more group theory, first W. ...

Capita Selecta in Geometry Moufang Quadrangles: Characterizations, Classification, Generalizations