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arXiv · 2312.02651

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

John van Bon
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Abstract

We construct a locally 5-arc transitive $G$-graph $Δ$, 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.

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John van Bon. 2023-12-05. A locally $5$-arc transitive graph related to ${\rm PSU}_3(8)$. https://arxiv.org/abs/2312.02651

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