TRANSITIVE DEFICIENCY ONE PARTIAL PARALLELISMS

Previously, Biliotti, Jha and Johnson classified all transitive deficiency one partial parallelisms in with the assumption that the Sylow p-subgroups, for p a prime, are ‘linear’. In this article, new arguments on elation and Baer p-groups show that the same results may be obtained without any assumptions on the transitive group. A corollary to this result shows that the classification theorem of Johnson on doubly transitive parallelisms in may be obtained without appealing to the classification theorem of finite simple groups.