engleski

Groups S-n x S-m in construction of flag-transitive block designs

In this paper, we observe the possibility that the group Sn × Sm acts as a flag-transitive automorphism group of a block design with point set {; ; ; 1, . . . , n}; ; ; ×{; ; ; 1, . . . , m}; ; ; , 4 ≤ n ≤ m ≤ 70. We prove the equivalence of that problem to the existence of an appropriately defined smaller flag-transitive incidence structure. By developing and applying several algorithms for the construction of the latter structure, we manage to solve the existence problem for the desired designs with nm points in the given range. In the vast majority of the cases with confirmed existence, we obtain all possible structures up to isomorphism.

combinatorial designs ; incidence structures ; automorphism groups

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