Subspaces intersecting each element of a regulus in one point, André-Bruck-Bose representation and clubs

الأصل · EN

In this paper results are proved with applications to the orbits of (n-1)-dimensional subspaces disjoint from a regulus of (n-1)-subspaces in (2n-1,q), with respect to the subgroup of (2n,q) fixing. Such results have consequences on several aspects of finite geometry. First of all, a necessary condition for an (n-1)-subspace U and a regulus of (n-1)-subspaces to be extendable to a Desarguesian spread is given. The description also allows to improve results in BaJa12 on the André-Bruck-Bose representation of a q-subline in (2,qⁿ). Furthermore, the results in this paper are applied to the classification of linear sets, in particular clubs.