Abstract

A new construction of parallelisms, determined by Johnson, is valid for both the finite and infinite cases and gives a variety of partial parallelisms of deficiency one that admit a transitive group. Since there are extensions to parallelisms, one obtains parallelisms admitting a collineation group fixing one spread and transitive on the remaining spreads. The construction permits a counting of the isomorphism classes of the parallelisms. In this article, we enumerate the isomorphism classes of the parallelisms and show that there are at least 1 + [(q - 3)/2r] mutually non-isomorphic parallelisms in PG(3, q = p r), for p odd. Furthermore, we provide a group-theoretic characterization of the constructed parallelisms. © 2002 Elsevier Science Ltd. All rights reserved.