Geodesic
Flag-transitive non-symmetric 2-designs with \((r, \lambda)=1\) and exceptional groups of Lie type
The electronic journal of combinatorics, Tome 27 (2020) no. 2
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This paper determines all pairs $(\mathcal{D},G)$ where $\mathcal{D}$ is a non-symmetric 2-$(v,k,\lambda)$ design with $(r,\lambda)=1$ and $G$ is the almost simple flag-transitive automorphism group of $\mathcal{D}$ with an exceptional socle of Lie type. We prove that if $T\trianglelefteq G\leq Aut(T)$ where $T$ is an exceptional group of Lie type, then $T$ must be the Ree group or Suzuki group, and there are five classes of designs $\mathcal{D}$.
DOI : 10.37236/8832
Classification : 05B05, 05B25, 20B25
Mots-clés : Suzuki group, Ree group, flag-transitive automorphism group 
@article{10_37236_8832,
     author = {Yongli Zhang and Shenglin Zhou},
     title = {Flag-transitive non-symmetric 2-designs with \((r, \lambda)=1\) and exceptional groups of {Lie} type},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {2},
     doi = {10.37236/8832},
     zbl = {1439.05037},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/8832/}
}
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Yongli Zhang; Shenglin Zhou. Flag-transitive non-symmetric 2-designs with \((r, \lambda)=1\) and exceptional groups of Lie type. The electronic journal of combinatorics, Tome 27 (2020) no. 2. doi: 10.37236/8832

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