Construction of symmetric designs admitting automorphisms of order p·q
by
Dean Crnkovic
University of Rijeka, Croatia
Coauthors: Sanja Rukavina (University of Rijeka)

Construction of symmetric (v, k, \lambda) designs admitting some automorphism group G consists of two steps. The first step is to find all orbit structures for parameters (v, k, \lambda) and the group G. The next step, called indexing, is to determine which points are incident with representatives of block orbits. We shall describe construction of symmetric designs with automorphism groups G =~ Z_p×Z_q, where p and q are primes. This method of construction is based on the use of principal series of these groups. The main idea is to decompose orbit structures for the group G to corresponding orbit structures for the group Z_p, and then proceed with indexing of those decomposed structures, having in mind the action of the group Z_q on the designs. In each phase of a construction it is necessary to use elements of a normalizer to eliminate mutually isomorphic structures. Using this method, number of symmetric designs are constructed, for example 2-(71, 15, 3), 2-(69, 17, 4) and 2-(61, 16, 4) designs with an automorphism of order 6 and 2-(66, 26, 10) designs with an automorphism of order 55.

Date received: March 10, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadz-53.