Vertex stabilizers of locally s-arc transitive graphs of pushing up type

Suppose that Delta is a thick, locally finite and locally s-arc transitive G-graph with s >= 4. For a vertex z in Delta, let G(z) be the stabilizer of z and G(z)([1]) be the kernel of the action of G(z) on the neighbours of z. We say Delta is of pushing up type provided there exists a prime p and a 1-arc (x,y) such that C-Gz(O-p(G(z)([1])))<= O-p(G(z)([1])) for z is an element of{x,y} and Op(G(x)([1]))<= O-p(G(y)([1])). We show that if Delta is of pushing up type, then O-p(G(x)([1])) is elementary abelian and G(x)/G(x)([1])congruent to X with PSL2(p(a))<= X <= P Gamma L-2(p(a)).