Flag-Transitive Non-Symmetric 2-Designs with $(r, \lambda)=1$ and Exceptional Groups of Lie Type
Keyword(s):
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 $\mathcal{D}$.
1993 ◽
pp. 89-102
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1979 ◽
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pp. 411-429
2019 ◽
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pp. 2050240
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Keyword(s):
2005 ◽
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2018 ◽
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