ABSTRACT
We now consider the possibility of doubly t-parallelisms, as well as transitive parallelisms. If there are t-parallelisms, for t > 2, it might be possible to discover them using group theory, for example, perhaps there are doubly transitive or transitive t-parallelisms. However, Johnson and Montinaro [143], [144] …rst proved that doubly transitive t-parallelisms imply that t = 2, and more recently proved the same result for transitive parallelisms. The doubly-transitive theorem uses the classi…cation theorem of doubly transitive groups, listed in the appendix. The very technical proof of the transitive theorem is sketched in the appendix by assembling the main building blocks of the proof. The reader is referred to Chapter 43 for the sketch of the proof.
