Local half Moufang 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...

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

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

Moufang-like conditions for generalized quadrangles and classification of all finite quasi-transitive generalized quadrangles

We tell the history ofMoufang generalized quadrangles.We review someMoufang-like conditions, and classify finite quasi-transitive generalized quadrangles. These are generalized quadrangles so that for any two non-concurrent linesU,V of theGQ, and for someW ∈ {U,V }⊥, the group of generalized homologies with axes U and V acts transitively on the points ofW incident with neither U nor V. As a by-...

Half-isomorphisms of Moufang Loops

We prove that if the squaring map in the factor loop of a Moufang loop Q over its nucleus is surjective, then every half-isomorphism of Q onto a Moufang loop is either an isomorphism or an anti-isomorphism. This generalizes all earlier results in this vein.