Moufang-like conditions for generalized quadrangles and classification of all finite quasi-transi\-tive generalized quadrangles
The authors give a very readable description of the history of generalized quadrangles which satisfy the Moufang condition, or some weaker condition, up to 2003. Moreover, they classify all finite thick generalized quadrangles which are quasi-transitive (this is a natural transitivity condition for generalized homologies). As a consequence they obtain the following result (without using the classification of finite simple groups): A finite thick generalized quadrangle is classical or dual classical if and only if it admits a BN-pair and a non-trivial homology.
scientific article; zbMATH DE number 2182141