Finite locally generalized quadrangles with affine planes
The first author and \textit{A. Pasini} [Eur. J. Comb. 13, No. 1, 39-57 (1992; Zbl 0749.51005)] characterized standard quotients of affine polar spaces of at least rank 4 (an affine polar space is a polar space with a geometric hyperplane removed; a standard quotient of it is a quotient w.r.t. to a group ``fixing the deleted geometric hyperplane'' pointwise). The main result of the paper under review is to extend this result to the rank 3 case (but only in the finite case). Basically, the author shows that every connected finite partial linear space containing affine planes and such that the set of lines and affine planes through any point forms a generalized quadrangle, is a standard quotient of a finite rank 3 affine polar space.
scientific article; zbMATH DE number 109274