Classification of linear spaces without three mutually parallel lines (Q917908)

From author's summary: ``We classify all finite linear spaces without three mutually parallel lines. Apart from two exceptions, such a space is necessarily a generalized projective plane, a simple extension of a generalized projective plane, or a complete inflated affine plane with a generalized projective plane at infinity.'' The details are too involved to be described here, the reader may find them in the original paper.