Block-transitive automorphism groups on 3-designs with small block size

2020/08/23 by Zhan, Xiaoqin, Yang, Meifang
#05B20 #20B25 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2008.09992

Abstract

The paper is an investigation of the structure of block-transitive automorphism groups of a 3-design with small block size. Let G be a block-transitive automorphism group of a nontrivial 3-(v,k,λ) design D with k≤ 6. We prove that if G is point-primitive then G is of affine or almost simple type. If G is point-imprimitive then D is a 3-(16,6,λ) design with λ∈\4, 12, 16, 24, 28, 48, 56, 64, 84, 96, 112, 140\, and rank(G)=3.

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