ABSTRACT
A ‘parallelism’ in PG(3,q) is a set of 1 + q -f q2 spreads which cover the lines. Hence, each line lies in exactly one of the spreads. More generally, a ‘parallelism in P G (3 ,if)’ where i f is a skewfield, is a set of line disjoint spreads which cover the line set of the projective geometry. Recall, when i f is a field, a spread S is said to be ‘regular’ exactly when the regulus generated by any three distinct lines of S is contained in S. A ‘regular parallelism’ is a parallelism where the spreads are all regular.
