A generalized quadrangle of order \((s,t)\) with center of transitivity is an elation quadrangle if \(s \leq t\) (Q1009007)

It is shown that a generalized quadrangle of order \((s,t)\) with a center of transitivity is an elation generalized quadrangle if \(s\leq t\). To obtain this result, the author generalizes a result of \textit{D. Frohardt} on Kantor's conjecture [J. Comb. Theory, Ser. A 46, No.~1, 139--145 (1988; Zbl 0639.51012)] from elation generalized quadrangles to the more general case of quadrangles with a center of transitivity.