We construct a locally 5-arc transitive $G$-graph $\Delta$, where $G \in \{\PSU_3(8) \sdp C_2, \PSU_3(8) \sdp C_6\}$. 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.
A locally 5-arc transitive graph related to PSU3(8)
van Bon J.
2024-01-01
Abstract
We construct a locally 5-arc transitive $G$-graph $\Delta$, where $G \in \{\PSU_3(8) \sdp C_2, \PSU_3(8) \sdp C_6\}$. 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.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
