engleski

Transitive designs constructed from groups

Let G be a finite permutation group acting transitively on the sets $\Omega_1$ and $\Omega_2$. We describe a construction of a 1-design determined by the action of G. G acts transitively on the set of points and the set of blocks of a constructed design. We apply this method to construct transitive designs from some finite simple groups. Some of the constructed 1-designs are also 2-designs. One can use this method to construct other combinatorial structures admitting transitive automorphism group, e.g. strongly regular graphs. Further, we discuss a construction of infinite designs from groups.

block design; regular graph; transitive group

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