# 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…

## 11 Citations

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

- Mathematics
- 2009

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…

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

- Mathematics
- 2007

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 ),…

### Line-transitive point-imprimitive linear spaces with number of points being a product of two primes

- Mathematics
- 2017

The work studies the line-transitive point-imprimitive automorphism groups of finite linear spaces, and is underway on the situation when the numbers of points are products of two primes. Let 𝒮 be a…

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

- MathematicsDes. Codes Cryptogr.
- 2008

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

- Mathematics
- 2001

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…

### Line-transitive point-imprimitive linear spaces with Fang-Li parameter gcd(k, r) at most ten

- Mathematics
- 2011

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…

### Line-transitive point-imprimitive linear spaces with Fang-Li parameter gcd(k, r) at most ten

- MathematicsFrontiers of Mathematics in China
- 2012

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…

### Line-primitive linear spaces with Fang-Li parameter gcd(k, r) at most 12

- Mathematics
- 2011

Let G be a subgroup of the automorphism group of a non-trivial finite linear space S. In this paper we prove that if G is line-primitive with Fang-Li parameter gcd(k, r) = 11 and 12, then G is also…

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