Abstract
Let \(\mathcal {S}\) be a finite thick generalized quadrangle, and suppose that G is an automorphism group of \(\mathcal {S}\). If G acts primitively on both the points and lines of \(\mathcal {S}\), then it is known that G must be almost simple. In this paper, we show that if the socle of G is \(\textrm{PSL}(2,q)\) with \(q\ge 4\), then \(q=9\) and \(\mathcal {S}\) is the unique generalized quadrangle of order 2.
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Acknowledgements
The authors thank John Bamberg for pointing out an error in an earlier version. They also thank the anonymous referees for their valuable comments and suggestions. This work was supported by National Natural Science Foundation of China (Grant Numbers 12171428 and 12225110).
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Communicated by C. E. Praeger.
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Feng, T., Lu, J. On finite generalized quadrangles with \(\textrm{PSL}(2,q)\) as an automorphism group. Des. Codes Cryptogr. 91, 2347–2364 (2023). https://doi.org/10.1007/s10623-023-01203-x
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DOI: https://doi.org/10.1007/s10623-023-01203-x