Abstract
In this paper we consider block-transitive automorphism groups of a 3-design with small block size. Let G be a block-transitive automorphism group of a nontrivial 3-\((v,k,\lambda )\) design \({\mathcal {D}}\) with \(k\le 6\). Then one of the following occurs:
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(i)
if G is point-primitive then G is of affine or almost simple type;
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(ii)
if G is point-imprimitive then G has rank 3 or 4, and \({\mathcal {D}}\) is a 3-\((16,6,\lambda )\) design with
$$\begin{aligned} \lambda \in \{4, 8, 12, 16, 24, 28, 32, 48, 56, 64, 80, 84, 96, 112, 128, 140, 160\}. \end{aligned}$$
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Acknowledgements
The author would like to express deepest gratitude to the anonymous referees for their careful reading and valuable comments.
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This work was supported by the National Natural Science Foundation of China (nos. 11801174 and 11961026).
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Zhan, X., Pang, X. & Wang, Y. Block-Transitive 3-Designs with Block Size At Most 6. Graphs and Combinatorics 38, 145 (2022). https://doi.org/10.1007/s00373-022-02544-5
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DOI: https://doi.org/10.1007/s00373-022-02544-5