A classification of finite partial linear spaces with a primitive rank 3 automorphism group of grid type

A partial linear space is a non-empty set of points, provided with a collection of subsets called lines such that any pair of points is contained in at most one line and every line contains at least two points. Graphs and linear spaces are particular cases of partial linear spaces. A partial linear space which is neither a graph nor a linear space is called proper. The aim of this paper is to classify the finite proper partial linear spaces with a primitive rank 3 automorphism group of grid type. (c) 2006 Elsevier Ltd. All rights reserved.