Conjugates for Finding the Automorphism Group and Isomorphism of Design Resolutions

Abstract

Consider a combinatorial design D with a full automorphism group G D.The automorphism group G of a design resolution R is a subgroup of G D.This subgroup maps each parallel class of R into a parallel class of R. Two resolutions R 1 and R 2 of D are isomorphic if some automorphismfrom G D maps each parallel class of R 1 to a parallel class of R 2. If G D isvery big, the computation of the automorphism group of a resolution and thecheck for isomorphism of two resolutions might be difficult. Such problems often arise when resolutions of geometric designs (the designs ofthe points and t-dimensional subspaces of projective or affine spaces) are considered.For resolutions with given automorphisms these problems can be solvedby using some of the conjugates of the predefined automorphisms. The method is explained in the present paper and an algorithm forconstruction of the necessary conjugates is presented.ACM Computing Classification System (1998): F.2.1, G.1.10, G.2.1.