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Flag-transitive and point-imprimitive designs with wreath product

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Abstract

This article studies 2-\((v,k,\lambda )\) designs admitting a point-imprimitive automorphism group \(H_0\wr H_1\), with the point set \(\Delta _0 \times \Delta _1\), where \(H_\ell \) is transitive on \(\Delta _\ell \), for \(\ell =0\), 1. We construct a family of such designs, characterize the structures of flag-transitive, point-imprimitive designs with such automorphism groups. As an application, we determine all flag-transitive, point-imprimitive 2-designs with block size of 8, showing that there are exactly fourteen such nonisomorphic designs.

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The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors would like to thank the anonymous referees for their valuable suggestions and comments which helped to improve this paper. This work was supported by the National Natural Science Foundation of China (Grant No. 11271173).

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  1. School of Mathematics, South China University of Technology, Guangzhou, 510641, People’s Republic of China

    Chuyi Zhong & Shenglin Zhou

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  1. Chuyi Zhong
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  2. Shenglin Zhou
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Correspondence to Shenglin Zhou.

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Zhong, C., Zhou, S. Flag-transitive and point-imprimitive designs with wreath product. J Algebr Comb 58, 231–245 (2023). https://doi.org/10.1007/s10801-023-01244-4

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  • DOI: https://doi.org/10.1007/s10801-023-01244-4

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