Non-symmetric 2-designs admitting a two-dimensional projective linear group

  • Xiaoqin Zhan
  • Shenglin Zhou


This paper is a contribution to the study of non-symmetric 2-designs admitting a flag-transitive automorphism group. We prove that if \(\mathcal {D}\) is a non-trivial non-symmetric 2-\((v, k, \lambda )\) design with \((r,\lambda ) = 1\) and \(G=PSL(2,q)\) acts flag-transitively on \(\mathcal {D}\), then up to isomorphism \(\mathcal {D}\) is a unique Witt-Bose-Shrikhande space, a unique 2-(6, 3, 2) design, a unique 2-(8, 4, 3) design, a unique 2-(10, 6, 5) design, or a unique 2-(28, 7, 2) design.


2-Design Non-symmetric Automorphism Flag-transitive Projective linear group 

Mathematics Subject Classification

05B05 05B25 20B25 



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. 11471123).


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Authors and Affiliations

  1. 1.School of ScienceEast China JiaoTong UniversityNanchangPeople’s Republic of China
  2. 2.School of MathematicsSouth China University of TechnologyGuangzhouPeople’s Republic of China

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