This analysis identifies block-transitive automorphism groups in designs, revealing sporadic simple groups' structure.
This paper contributes to the classification of non-trivial \(2\)-designs with block size \(5\) admitting a block-transitive automorphism group. Let \({ D=(P,B)}\) be a non-trivial 2-\((v,5,λ)\) design and \(G\) be a block-transitive automorphism group of \(D\). The main aim of this paper is to determine all pairs \((D,G)\) when Soc(\(G\)) is a sporadic simple group.
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Lei et al. (2025) studied this question.
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