On the nonexistence of certain Hughes generalized quadrangles

@article{Kaey2007OnTN,
  title={On the nonexistence of certain Hughes generalized quadrangles},
  author={Joris De Kaey and Alan Offer and Hendrik Van Maldeghem},
  journal={Designs, Codes and Cryptography},
  year={2007},
  volume={44},
  pages={87-96}
}
In this paper, we prove that the Hermitian quadrangle $${\mathsf{H}}(4, q^2)$$ is the unique generalized quadrangle Γ of order (q2, q3) containing some subquadrangle of order (q2, q) isomorphic to $${\mathsf{H}}(3, q^2)$$ such that every central elation of the subquadrangle is induced by a collineation of Γ. 

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