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

Abstract

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 not a graph or a linear space is called proper. In this paper, we give a complete classification of all finite proper partial linear spaces admitting a primitive rank $3$ automorphism group of almost simple type.