Inequalities involving the Delandtsheer–Doyen parameters for finite line-transitive linear spaces
نویسندگان
چکیده
منابع مشابه
Inequalities involving the Delandtsheer-Doyen parameters for finite line-transitive linear spaces
The paper studies line-transitive, point-imprimitive automorphism groups G of finite linear spaces. In particular, it explores inequalities involving two integer parameters x; y introduced by Delandtsheer and Doyen associated with a given G-invariant partition C of the point set. There is special interest in the case where C is G-normal, that is, C is the set of orbits of a normal subgroup of G...
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Until the 1990’s the only known finite linear spaces admitting line-transitive, pointimprimitive groups of automorphisms were Desarguesian projective planes and two linear spaces with 91 points and line size 6. In 1992 a new family of 467 such spaces was constructed, all having 729 points and line size 8. These were shown to be the only linear spaces attaining an upper bound of Delandtsheer and...
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In this paper we prove the following theorem. Let S be a linear space. Assume that S has an automorphism group G which is line-transitive and point-imprimitive with k < 9. Then S is one of the following:(a) A projective plane of order 4 or 7, (a) One of 2 linear spaces with v = 91 and k = 6, (b) One of 467 linear spaces with v = 729 and k = 8. In all cases the full automorphism group Aut(S) is ...
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We present a partial classification of those finite linear spaces S on which an almost simple group G with socle PSL(3, q) acts line-transitively. A linear space S is an incidence structure consisting of a set of points Π and a set of lines Λ in the power set of Π such that any two points are incident with exactly one line. The linear space is called non-trivial if every line contains at least ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2003
ISSN: 0097-3165
DOI: 10.1016/s0097-3165(03)00012-8