Isomorphism and Invariants of Parallelisms of Projective Spaces

Abstract

We consider the computer-aided constructive classification of parallelisms with predefined automorphism groups in small finite projective spaces. The usage of a backtrack search algorithm makes it very important to filter away equivalent partial solutions as soon as possible and to use a fast method for checking for isomorphism of any two parallelisms. The rejection of most of the equivalent solutions can be done by a test which uses the normalizer of the predefined automorphism group. We consider the applicability and effectiveness of such a test, and present sensitive invariants of resolutions of Steiner 2-designs. They can be used to facilitate any type of test for isomorphism of parallelisms.