Camina-Gagen 定理 for Steiner 5-designs
摘要
A famous Camina-Gagen 定理 is that if $G$ acts as a block-transitive group of automorphisms of a $2$-$(v,k,1)$ design with $k\mid~v$, then $G$ is flag-transitive.In this paper, we generalize this 定理 to $5$-$(v,k,1)$ designs.We prove that if $G$ acts block-transitively on a non-trivial $5$-$(v,k,1)$ design ${D}$ with $k\mid~v$, then ${D}$ is flag-transitive.
引用本文（GB/T 7714）
Huang Zheng, Weijun Liu, Lihua Feng. Camina-Gagen 定理 for Steiner 5-designs[J]. Scientia Sinica Mathematica, 2022.
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