Block-transitive 3-designs Associated with Alternating Groups
A t-(v,k,λ)design is said to be G-point-primitive or G-block-transitive,if its automorphism group G acts primitively on the point set or transitively on the block set,respectively.In this paper we begin by extending some results on block-transitive Steiner 2-designs to block-transitive 3-designs,and then based on these results,investigate the G-point-primitive block-transitive 3-(v,k,λ)designs for alternating or symmetric groups G.We prove that when n ≥ min{λ2,30} the point stabilizer in G must be of intransitive type,and specifically,when n ≥ 30 there exists no nontrivial G-point-primitive block-transitive 3-(v,k,2)design.
Block-transitive designPrimitive groupAlternating group
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