#### Vol. 4, No. 1, 2006

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On a characterization of the finite twisted triality hexagons using one classical ideal split Cayley subhexagon

### Joris De Kaey, Alan Darryl Offer and Hendrik J. van Maldeghem

Vol. 4 (2006), No. 1, 27–52
##### 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
generalized hexagons, central collineations, root elations, little projective group
Primary: 51E12
##### Milestones
Received: 20 October 2006
Accepted: 8 January 2007
##### Authors
 Joris De Kaey Alan Darryl Offer Hendrik J. van Maldeghem Vakgroep Zuivere Wiskunde en Computeralgebra University of Ghent 9000 Gent Belgium