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Abstract
A partial linear space is a pair (Formula presented.) where (Formula presented.) is a nonempty set of points and (Formula presented.) is a collection of subsets of (Formula presented.) 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 (Formula presented.) of a proper partial linear space acts transitively on ordered pairs of distinct collinear points and ordered pairs of distinct noncollinear points precisely when (Formula presented.) 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 (Formula presented.). 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.
Original language  English 

Pages (fromto)  10111084 
Number of pages  74 
Journal  Journal of the London Mathematical Society 
Volume  104 
Issue number  3 
Early online date  5 May 2021 
DOIs  
Publication status  Published  Oct 2021 
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Dive into the research topics of 'Partial linear spaces with a rank 3 affine primitive group of automorphisms'. Together they form a unique fingerprint.Projects
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Partial linear spaces with a rank 3 affine primitive group of automorphisms
Bamberg, J., Devillers, A., Fawcett, J. B. & Praeger, C. E., 29 Aug 2019, arXiv, (J. London Math. Soc.).Research output: Working paper › Preprint
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