Intersection pattern of Ree subgroups in G2(q), q = 32n+l > 3

Throughout this paper, we fix a finite group X isomorphic to G2(q),q = 32n+1 > 3 and a subgroup G of X isomorphic to the Ree group 2G2(q). It is well-known that X contains a unique conjugacy class C of maximal subgroups with the property that each member of C is isomorphic to G ([7], Theorem A, p.33) and is the set-stabilizer in X of a Ree-Tits ovoid of the (q, q) - generalized hexagon H associated with X for the natural action of X on the points of H ([12], see also [4]). In this paper, we study the permutation representation of X on the set of the Ree-Tits ovoids of H.