ON PARALLELISMS OF ODD DIMENSIONAL FINITE PROJECTIVE SPACES

Abstract

In this paper we give a new, simple and explicit proof of a theorem of Baker. This states that every odd dimensional projective space over the field of two elements admits a 1-packing of 1-spreads, i.e. a partition of its lines into families of mutual disjoint lines whose union covers the space. This 1-packing may be generated from anyone of its spreads by repeated application of a fixed collineation.