A locally $5$-arc transitive graph related to ${\rm PSU}_3(8)$

John van Bon

A locally $5$-arc transitive graph related to ${\rm PSU}_3(8)$

Combinatorics 2023-12-06 v1 Group Theory

Authors: John van Bon

Abstract

We construct a locally 5-arc transitive $G$ -graph $\Delta$ , where $G \in \{ {\rm PSU}_3(8) \rtimes C_2, {\rm PSU}_3(8) \rtimes C_6\}$ . 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

locally 5-arc transitive graph PSU3(8) vertex stabilizer amalgam local characteristic 3 non-split extension weak BN-pair

Cite

@article{arxiv.2312.02651,
  title  = {A locally $5$-arc transitive graph related to ${\rm PSU}_3(8)$},
  author = {John van Bon},
  journal= {arXiv preprint arXiv:2312.02651},
  year   = {2023}
}

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