The twisted cubic in PG(3, q) and translation spreads in H(q)

Using the connection between translation spreads of the classical generalized hexagon H(q) and the twisted cubic of PG(3,q), established in [European J. Combin. 23 (2002) 367-376], we prove that if q^n=1(mod3), q odd, q>=4n^2-8n+2 and n>2, then H(q^n) does not admit an F"q-translation spread.

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