Abstract
This paper contributes to the classification of flag-transitive 2-designs. Let \(\mathcal {D}\) be a 2-\((v,k,\lambda )\) design with prime square replication number. Suppose that G is a flag-transitive, point-primitive automorphism group of \(\mathcal {D}\) with socle an alternating group. We prove that \(\mathcal {D}\) is the unique 2-(10, 6, 5) design with \(G=Alt(6)\) or Sym(6).
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Acknowledgements
The authors would like to thank anonymous referees for providing us valuable and helpful comments and suggestions.
Funding
This work is supported by the National Natural Science Foundation of China (Grant number: 12201469).
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Communicated by L. Teirlinck.
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Shen, J., Chen, J. & Zhou, S. Flag-transitive 2-designs with prime square replication number and alternating groups. Des. Codes Cryptogr. 91, 709–717 (2023). https://doi.org/10.1007/s10623-022-01121-4
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DOI: https://doi.org/10.1007/s10623-022-01121-4