# 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}
}```
• Published 1 September 2007
• Mathematics, Geology
• Designs, Codes and Cryptography
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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Let 0 be a finite generalized quadrangle of order (q, q2), and suppose that it has a subquadrangle 1 isomorphic to Q(4, q). We show that 0 is isomorphic to the classical generalized quadrangle Q(5,
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Let ? be a finite generalized quadrangle of order (q,q2 ), and suppose that it has a subquadrangle ? isomorphic to Q(4,q ). We show that ? is isomorphic to the classical generalized quadrangle Q(5,q