Low rank groups of Lie type acting point and line-primitively on finite generalised quadrangles

Suppose we have a finite thick generalised quadrangle whose automorphism group G acts primitively on both the set of points and the set of lines. Then G must be almost simple. In this paper, we show that soc(G) cannot be isomorphic to Sz(2²ᵐ⁺¹) or Ree(3²ᵐ⁺¹) where m is a positive integer.