ABSTRACT
In this chapter, we give the important construction of Beutelspacher of parallelisms of PG(2r 1; q), and generalize the construction to arbitrary skew…elds. This chapter is a modi…cation of the author’s work [108]. In 1974, Buetelspacher [16] gave a construction of parallelisms in
PG(2r 1; q), for any positive integer r and for any prime power q = pt > 2. We o¤er a generalization of Buetelspacher’s construction to arbitrary projective spaces over skew…elds and construct a variety of new parallelisms.
