Embeddings of flag-transitive classical locally polar geometries of rank 3
The author considers finite flag-transitive extended (classical and thick) generalized quadrangles, which are all classified, and determines all group-admissable embeddings of such geometries. An embedding here is what the author calls a (2,1)-embedding: the elements having a (circle)- geometry as residue are certain points of a projective space; the elements having a generalized digon as residue must then be full lines of the projective space. Group-admissable just means that the embedding preserves the automorphism group of the extended generalized quadrangle. The proof of the main result (the determination of all group-admissable embeddings of finite flag-transitive classical extended generalized quadrangles) is very group related. But the paper can also serve as a survey on finite flag-transitive classical extended generalized quadrangles.
flag-transitive classical extended generalized quadrangles
scientific article; zbMATH DE number 93780