engleski

Construction of Symmetric Designs Admitting Automorphisms of Order pxq

Construction of symmetric (v, k, \lambda) designs admitting some automorphism group G consist 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 the representative of block orbits. We shall describe the construction of symmetric designs with automorphism groups G isomorphic to Z_p x Z_q, where p and q are primes. The 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 the 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 the construction it is necessary to use elements of a normalizer to eliminate mutually isomorphic structures. Using this method, a 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.

symmetric design; automorphism group; orbit structure

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