A characterization of the split Cay ley generalized hexagon H(q) using one subhexagon of order (1, q)

摘要

In this paper, we prove that, if a generalized hexagon F of order q contains a subhexagon F' (of order (1, q)) isomorphic to the incidence graph of the Desarguesian plane PG(2, q), and if the automorphism group of F stabilizing F1 induces all elations in PG(2, q), then F must be isomorphic to the split Cayley hexagon H(q).