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This paper is a further contribution to the classification of linetransitive finite linear spaces. We prove that if ? is a non-trivial finite linear space such that the Fang-Li parameter gcd(k, r) is 9 or 10, and the group G ? Aut(?) is line-transitive and point-imprimitive, then ? is the Desarguesian projective plane PG(2, 9).  相似文献
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A non-regular primitive permutation group is called extremely primitive if a point stabilizer acts primitively on each of its nontrivial orbits. Let S be a nontrivial finite regular linear space and G ≤ Aut(S). Suppose that G is extremely primitive on points and let rank(G) be the rank of G on points. We prove that rank(G) ≥ 4 with few exceptions. Moreover, we show that Soc(G) is neither a sporadic group nor an alternating group, and G = PSL(2, q) with q + 1 a Fermat prime if Soc(G) is a finite classical simple group.  相似文献
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