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Flag-transitive block designs with prime replication number and almost simple groups

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Abstract

In this article, we study 2-designs with prime replication number admitting a flag-transitive automorphism group. The automorphism groups of these designs are point-primitive of almost simple or affine type. We determine 2-designs with prime replication number admitting an almost simple automorphism group and prove that such a design belongs to one of two infinite families of projective spaces or Witt-Bose-Shrikhande spaces or it is isomorphic to a design with parameters (6, 3, 2), (8, 4, 3), (11, 5, 2) or (12, 6, 5).

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Acknowledgements

The authors would like to thank anonymous referees for providing us helpful and constructive comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran

    Seyed Hassan Alavi, Mohsen Bayat, Jalal Choulaki & Ashraf Daneshkhah

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  1. Seyed Hassan Alavi
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  2. Mohsen Bayat
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  3. Jalal Choulaki
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  4. Ashraf Daneshkhah
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Correspondence to Seyed Hassan Alavi.

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Communicated by C. E. Praeger.

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Alavi, S.H., Bayat, M., Choulaki, J. et al. Flag-transitive block designs with prime replication number and almost simple groups. Des. Codes Cryptogr. 88, 971–992 (2020). https://doi.org/10.1007/s10623-020-00724-z

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