Line-Transitive Point-Imprimitive Linear Spaces with Fang-Li Parameter gcd$(k,r)$ at most $12$

Abstract

This paper investigates the finite line-transitive point-imprimitive linear spaces. Let $S$ be a non-trivial finite line-transitive point-imprimitive linear space with the Fang-Li parameter $k^{(r)}=11$ or $12$. Our conclusion is that $\mathcal{S}$ is a Desarguesian projective plane PG(2,11).