The transitive t-parallelisms of a finite projective space

摘要

The transitive t-parallelisms of PG _n(q) are shown to exist only for t = 1, (t, n, q) = (2, 5, 2) and possibly for (t, n, q) = (2, 5, 3). Moreover, the structure of the collineation group of PG _n(q) acting transitively on the parallelism is completely determined, and a new infinite class of transitive parallelisms of PG _n(2) is provided.