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

John van Bon, Chris Parker

Suppose that $\Delta$ a thick, locally finite and locally $s$-arc transitive $G$-graph with $s\ge 4$. For a vertex $z$ in $\Delta$, let $G_z$ be the stabilizer of $z$ and $G_z^{[1]}$ be the…