One-point extensions of polar spaces
The authors combinatorially characterize one-point extensions of finite, thick, non-degenerate polar spaces of rank at least 3. It is proved that in this case the polar space is defined over GF(2) and an explicit construction of the one-point extension is given. This gives a more elementary proof (not involving group-theoretic methods) of F. Buekenhout's result on the uniqueness of one-point extensions of classical polar spaces [\textit{F. Buekenhout}, Geom. Dedicata 6, No.1, 13- 21 (1977; Zbl 0363.05056)]. Using their characterization the authors further show that the automorphism group of a one-point extension of a finite, thick, non-degenerate polar space of rank at least 3 is a one- point extension of the automorphism group of the polar space.
scientific article; zbMATH DE number 4210938