Groups of projectivities of generalized quadrangles
For some reason the study of groups of projectivities of generalized quadrangles did not yet receive the attention due, although the study of groups of projectivities of projective planes produced a number of remarkable classification results. This paper rights this wrong. Characterizations of some classical generalized quadrangles with regular points or lines by properties of the group of projectivities are given. In particular, all finite classical generalized quadrangles with regular lines and all symplectic quadrangles over quadratically closed fields are characterized. The proof of the results employs the coordinatization of generalized quadrangles introduced by \textit{G. Hanssens} and \textit{H. Van Maldeghem} [Ann. Discrete Math. 37, 195-207 (1988; Zbl 0643.51011)].
scientific article; zbMATH DE number 1240980