Conjugates for Finding the Automorphism Group and Isomorphism of Design Resolutions


  • Svetlana Topalova Institute of Mathematics and Informatics Bulgarian Academy of Sciences P.O. Box 323 5000 Veliko Tarnovo, Bulgaria



conjugates, design resolutions, parallelisms, automorphism group


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 automorphism
from G D maps each parallel class of R 1 to a parallel class of R 2. If G D is
very big, the computation of the automorphism group of a resolution and the
check for isomorphism of two resolutions might be difficult.

Such problems often arise when resolutions of geometric designs (the designs of
the points and t-dimensional subspaces of projective or affine spaces) are considered.

For resolutions with given automorphisms these problems can be solved
by using some of the conjugates of the predefined automorphisms.
The method is explained in the present paper and an algorithm for
construction of the necessary conjugates is presented.

ACM Computing Classification System (1998): F.2.1, G.1.10, G.2.1.