Abstract
This paper is a contribution to the classification of flag-transitive 2-\((v,4,\lambda )\) designs. We determine all such designs admitting \(G=PSL(2,q)\) as a flag-transitive automorphism group.
Similar content being viewed by others
References
Alavi S.H., Bayat M., Daneshkhah A.: Symmetric designs admitting flag-transitive and point-primitive automorphism groups associated to two dimensional projective special groups. Des. Codes Cryptogr. 79(2), 337–351 (2016).
Bamberg J., Giudici M., Liebeck M.W., Praeger C.E., Saxl J.: The classification of almost simple \(\frac{3}{2}\)-transitive groups. Trans. Am. Math. Soc. 365(8), 4257–4311 (2013).
Colbourn C.J., Dinitz J.H.: The CRC Handbook of Combinatorial Designs. CRC Press, Boca Raton, FL (2007).
Cusack C.A., Graham S.W., Kreher D.L.: Large sets of 3-designs from \(PSL(2, q)\), with block sizes 4 and 5. J. Comb. Des. 3(2), 147–160 (1995).
Davies H.: Flag-transitivity and primitivity. Discret. Math. 63, 91–93 (1987).
Delandtsheer A.: Flag-transitive finite simple groups. Arch. Math. 47, 395–400 (1986).
Huber M.: A census of highly symmetric combinatorial designs. J. Algebr. Comb. 26, 453–476 (2007).
Kantor W.M., Liebler R.A.: The rank 3 permutation representations of the finite classical groups. Trans. Am. Math. Soc. 271, 1–71 (1982).
Keranen M.S., Kreher D.L., Shiue P.J.-S.: Quadruple systems of the projective special linear group \(PSL(2, q)\), \(q\equiv 1\) (mod 4). J. Comb. Des. 11(5), 339–351 (2003).
Keranen M.S., Kreher D.L.: 3-designs of \(PSL(2,2^n)\) with block sizes 4 and 5. J. Comb. Des. 12(2), 103–111 (2004).
Liu W.J., Tang J.X., Wu Y.X.: Some new 3-designs from \(PSL(2, q)\) with \(q\equiv 1\) (mod 4). Sci. China Math. 55(9), 1901–1911 (2012).
Tang J.X., Liu W.J., Wang J.H.: Groups \(PSL(n, q)\) and 3-\((v, k,1)\) designs. Ars Comb. 110, 217–226 (2013).
Zhan X.Q., Zhou S.L.: Non-symmetric 2-designs admitting a two-dimensional projective linear group. Des. Codes Cryptogr. 86(12), 2765–2773 (2018).
Acknowledgements
The authors would like to thank referees for providing us helpful and constructive comments and suggestions, which led to the improvement of the article. This work is supported by the National Natural Science Foundation of China (Grant No. 11801174).
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by L. Teirlinck.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Zhan, X., Ding, S. & Bai, S. Flag-transitive 2-designs from PSL(2, q) with block size 4. Des. Codes Cryptogr. 87, 2723–2728 (2019). https://doi.org/10.1007/s10623-019-00648-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10623-019-00648-3