Assuming that the classification theorem for finite simple groups is complete, a conjecture of M. Hall (Proc. Sympos. Pure Math. 6 (1962), 47-66; and in “Proceedings of the International Conference… (More)

Let the point-line geometry Γ = (P ,L) be a half-spin geometry of type Dn,n. Then, for every embedding of Γ in the projective space P(V ), where V is a vector space of dimension 2n−1, it is true that… (More)

One says that Veldkamp lines exist for a point-line geometry Γ if, for any three distinct (geometric) hyperplanes A, B and C (i) A is not properly contained in B and (ii) A ∩ B ⊆ C implies A ⊂ C or A… (More)

There are two basic theorems. Let G be a strong parapolar space with these three properties: (1) For each point x and symplecton S, x is collinear to some point of S. (2) The set of points at… (More)

Described here are constructions of finite geometries, with special emphasis on generalized quadrangles, using first a strange subset <# of flags of a known finite geometry and then defining new… (More)

Several problems are introduced. They are not “by the wayside” in the sense that they were once considered and later discarded. They are very much alive. They are by the wayside, because I believe… (More)

We give a construction which takes a rank two incidence geometry with three points on a line and returns a geometry of the same type, i.e., with three points on a line. It is also demonstrated that… (More)