# Finite line-transitive linear spaces: parameters and normal point-partitions

@article{Delandtsheer2003FiniteLL, title={Finite line-transitive linear spaces: parameters and normal point-partitions}, author={Anne Delandtsheer and Alice C. Niemeyer and Cheryl E. Praeger}, journal={Advances in Geometry}, year={2003}, volume={3}, pages={469-485} }

Until the 1990's the only known finite linear spaces admitting line-transitive, point- imprimitive 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 Doyen on the number of points. Projective planes, and the linear spaces just mentioned on 91 or 729…

## 10 Citations

### Finite line-transitive linear spaces: Theory and search strategies

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The paper summarises existing theory and classifications for finite line-transitive linear spaces, develops the theory further, and organises it in a way that enables its effective application. The…

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### Linear spaces with a line-transitive point-imprimitive automorphism group and Fang-Li parameter gcd(k,r) at most eight

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In 1991, Weidong Fang and Huiling Li proved that there are only ﬁnitely many non-trivial linear spaces that admit a line-transitive, point imprimitive group action, for a given value of gcd( k, r ),…

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### Classification of line-transitive point-imprimitive linear spaces with line size at most 12

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In this paper we complete a classification of finite linear spaces $${\mathcal{S}}$$ with line size at most 12 admitting a line-transitive point-imprimitive subgroup of automorphisms. The examples…

### Implications of Line-Transitivity for Designs

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For a t-design D(t≥2) transitivity of a group G of automorphisms on the blocks (or lines) of D implies transitivity on points. Delandtsheer and Doyen proved in 1989 that if in addition the group G…

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This paper is a further contribution to the classification of linetransitive finite linear spaces. We prove that if ℐ is a non-trivial finite linear space such that the Fang-Li parameter gcd(k, r) is…

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