Moufang Quadrangles of Mixed type

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. ...

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

Departing from a Moufang set related to a polarity in an exceptional Moufang quadrangle of type F4, we construct a rank three geometry. The main property of this new geometry is that its automorphism group is identical to the one of the underlying Moufang set, providing a tool to study this Moufang set in a geometrical way. As a corollary we obtain that every automorphism of an exceptional Mouf...

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

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