Geodesic
Flag-transitive point-primitive symmetric \((v,k,\lambda)\) designs with bounded \(k\)
Zhilin Zhang1 ; Pingzhi Yuan2 ; Shenglin Zhou3
1School of Mathematical Science, South China Normal University
2South China Normal University
3South China University of Technology
The electronic journal of combinatorics, Tome 27 (2020) no. 4
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In 2012, Tian and Zhou conjectured that a flag-transitive and point-primitive automorphism group of a symmetric $(v,k,\lambda)$ design must be an affine or almost simple group. In this paper, we study this conjecture and prove that if $k\leqslant 10^3$ and $G\leqslant Aut(\mathcal{D})$ is flag-transitive, point-primitive, then $G$ is affine or almost simple. This support the conjecture.
DOI : 10.37236/9335
Classification : 05B05, 05B25, 20B25
Mots-clés : symmetric design, flag-transitive design, point-primitive design

Zhilin Zhang  1   ; Pingzhi Yuan  2   ; Shenglin Zhou  3

1 School of Mathematical Science, South China Normal University
2 South China Normal University
3 South China University of Technology 
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     author = {Zhilin Zhang and Pingzhi Yuan and Shenglin Zhou},
     title = {Flag-transitive point-primitive symmetric \((v,k,\lambda)\) designs with bounded \(k\)},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {4},
     doi = {10.37236/9335},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/9335/}
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Zhilin Zhang; Pingzhi Yuan; Shenglin Zhou. Flag-transitive point-primitive symmetric \((v,k,\lambda)\) designs with bounded \(k\). The electronic journal of combinatorics, Tome 27 (2020) no. 4. doi: 10.37236/9335

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