Block-transitive 3-(v,k,1) designs associated with alternating groups

2022/08/01 by Lan, Ting, Liu, Weijun, Yin, Fu-Gang
#05B05 #20B25 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2208.00670

Abstract

Let D be a nontrivial 3-(v,k,1) design admitting a block-transitive group G of automorphisms. A recent work of Gan and the second author asserts that G is either affine or almost simple. In this paper, it is proved that if G is almost simple with socle an alternating group, then D is the unique 3-(10,4,1) design, and G=PGL(2,9), M₁₀ or Aut(A₆ )=S₆:Z₂, and G is flag-transitive.

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