Almost simple groups with socle Ree(q) acting on finite linear spaces

This article is part of a project set up to classify groups and linear spaces where the group acts transitively on the lines of the space. Let GG be an automorphism group of a linear space. We know that the study of line-transitive finite linear spaces can be reduced to three cases, distinguishable by means of properties of the action on the point-set: that in which GG is of affine type in the sense that it has an elementary abelian transitive normal subgroup; that in which GG has an intransitive minimal normal subgroup; and that in which GG is almost simple, in the sense that there is a simple transitive normal subgroup TT in GG whose centraliser is trivial, so that T⊴G≤Aut(T). In this paper we treat almost simple groups in which TT is a Ree group and obtain the following theorem:Let T⊴G≤Aut(T), and let SS be a finite linear space on which GG acts as a line-transitive automorphism group. If TT is isomorphic to G22(q), then TT is line-transitive and SS is a Ree unitary space.