engleski

Transitive designs constructed from finite groups

Let G be a finite group. We describe a construction of 1-designs admitting an automorphism group isomorphic to G. The designs are constructed by defining incidence structures on conjugacy classes of subgroups of the group G. The group G acts transitively on the set of points and the set of blocks of the constructed design. Some of the constructed 1-designs are also 2-designs. We apply this method to construct transitive 2-designs from some finite simple groups. One can use this method to construct other combinatorial structures admitting transitive automorphism group, e.g. strongly regular graphs. Keywords: Transitive designs, finite group, automorphism group.

combinatorial design; strongly regular graph

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