Constructions for point-regular linear spaces

We introduce the concept of simple difference family over a group G and relative to a partial spread in G. Such a family generates a point-regular linear space, i.e. a linear space with an automorphism group acting regularly on the point-set. In particular, we prove that any abelian linear space is generated by such a family. Using this new notion of difference family, we give a number of recursive constructions for point-regular linear spaces.