@techreport{c71772c10e6c4bd7a6eb193d63c5060e,
title = "Partial linear spaces with a rank 3 affine primitive group of automorphisms",
abstract = " A partial linear space is a pair $(\mathcal{P},\mathcal{L})$ where $\mathcal{P}$ is a non-empty set of points and $\mathcal{L}$ is a collection of subsets of $\mathcal{P}$ called lines such that any two distinct points are contained in at most one line, and every line contains at least two points. A partial linear space is proper when it is not a linear space or a graph. A group of automorphisms $G$ of a proper partial linear space acts transitively on ordered pairs of distinct collinear points and ordered pairs of distinct non-collinear points precisely when $G$ is transitive of rank 3 on points. In this paper, we classify the finite proper partial linear spaces that admit rank 3 affine primitive automorphism groups, except for certain families of small groups, including subgroups of $A\Gamma L_1(q)$. Up to these exceptions, this completes the classification of the finite proper partial linear spaces admitting rank 3 primitive automorphism groups. We also provide a more detailed version of the classification of the rank 3 affine primitive permutation groups, which may be of independent interest. ",
keywords = "math.GR, math.CO, 51E30, 05E18, 20B15, 05B25, 20B25",
author = "John Bamberg and Alice Devillers and Fawcett, {Joanna B.} and Praeger, {Cheryl E.}",
note = "In this version, we have removed the assumption $V\leq H$ from 18.1 (old 13.2) and we have a new elementary proof of 10.10 (old 13.1). We have also reorganised some of the sections and made minor revisions throughout. 69 pages, 1 figure",
year = "2019",
month = aug,
day = "29",
language = "English",
series = "J. London Math. Soc.",
publisher = "arXiv",
address = "United States",
type = "WorkingPaper",
institution = "arXiv",
}