Point-Transitive Linear Spaces
Received:January 27, 2018  Revised:July 17, 2018
Key Word: linear space   design   automorphism group   point-transitive
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.11801311; 11626141).
 Author Name Affiliation Haiyan GUAN Department of Mathematics, China Three Gorges University, Hubei 443002, P. R. China Three Gorges Mathematical Research Center, Hubei 443002, P. R. China
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This work is a contribution to the classification of linear spaces admitting a point-transitive automorphism group. Let ${\mathcal{S}}$ be a regular linear space with 51 points, with lines of size 6, and $G$ be an automorphism group of ${\mathcal{S}}$. We prove that $G$ cannot be point-transitive.