Generalised Polygons Admitting a Point-Primitive Almost Simple Group of Suzuki or Ree Type

Let G be a collineation group of a thick finite generalised hexagon or generalised octagon Γ. If G acts primitively on the points of Γ, then a recent result of Bamberg et al. shows that G must be an almost simple group of Lie type. We show that, furthermore, the minimal normal subgroup S of G cannot be a Suzuki group or a Ree group of type G2, and that if S is a Ree group of type F4, then Γ is (up to point–line duality) the classical Ree–Tits generalised octagon.