A locally 5-arc transitive graph related to PSU₃(8)

Abstract

We construct a locally 5-arc transitive G-graph Δ, where $G\in \{{\text{PSU}}_3(8)⋊C_2,{\text{PSU}}_3(8)⋊C_6\}$. The corresponding vertex stabilizer amalgams are of local characteristic 3 but are not weak (B, N)-pairs. They are the first examples of this kind where there exists a vertex z such that the extension of $G_z/O_p(G_z^{[1]})$ over $O_p(G_z^{[1]})$ is non-split.

Keywords:

• Group amalgams
• locally s-arc transitive graphs

2020 Mathematics Subject Classification:

• 05C25
• 05E18
• 20B25

Disclosure statement

There are no competing interests to declare.