Groups \(S_n \times S_m\) in construction of flag-transitive block designs
Keyword(s):
In this paper, we observe the possibility that the group \(S_{n}\times S_{m}\) acts as a flag-transitive automorphism group of a block design with point set \(\{1,\ldots ,n\}\times \{1,\ldots ,m\},4\leq n\leq m\leq 70\). 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.
1993 ◽
pp. 89-102
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1979 ◽
Vol 27
(4)
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pp. 411-429
2019 ◽
Vol 19
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pp. 2050240
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2005 ◽
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(1)
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pp. 191-196
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1985 ◽
Vol 38
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pp. 192-202
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1979 ◽
Vol 48
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pp. 171-202
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1993 ◽
Vol 25
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pp. 1-6
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