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

Let Δ be a generalized hexagon of order (q3,q), for some prime power q not divisible by 3. Suppose that Δ contains a subhexagon Γ of order (q,q) isomorphic to a split Cayley hexagon (associated to Dickson’s group G2(q)), and suppose that every axial elation (long root elation) in Γ is induced by Aut(Δ)Γ. Then we show that Δ is isomorphic to the twisted triality hexagon T(q3,q) associated to the group 3D4(q).

generalized hexagons, central collineations, root elations, little projective group
Mathematical Subject Classification 2000
Primary: 51E12
Received: 20 October 2006
Accepted: 8 January 2007
Joris De Kaey
Alan Darryl Offer
Hendrik J. van Maldeghem
Vakgroep Zuivere Wiskunde en Computeralgebra
University of Ghent
9000 Gent