Abstract

Let $\Delta$ be a generalized hexagon of order $\left(q^3,q\right)$, for some prime power $q$ not divisible by $3$. Suppose that $\Delta$ contains a subhexagon $\Gamma$ of order $\left(q,q\right)$ isomorphic to a split Cayley hexagon (associated to Dickson’s group ${\mathsf{G}}_2\left(q\right)$), and suppose that every axial elation (long root elation) in $\Gamma$ is induced by Aut${\left(\Delta \right)}_{\Gamma }$. Then we show that $\Delta$ is isomorphic to the twisted triality hexagon $\mathsf{T}\left(q^3,q\right)$ associated to the group ${}^3{\mathsf{D}}_4\left(q\right)$.

Keywords

Mathematical Subject Classification 2000

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