A theorem concerning nets arising from generalized quadrangles with a regular point (Q1862442)

Consider a generalized quadrangle of order \((s,t)\), \(s,t\neq 1\), with a regular point. Then there is a net which arises from this regular point. The author proves that if such a net has a proper subnet with the same degree as the net, then it must be an affine plane of order \(t\). Also, this affine plane induces a proper subquadrangle of order \(t\) containing the regular point, implying that \(s=t^2\). The author then applies these results to the theory of symmetries of generalized quadrangles, presenting results on elation generalized quadrangles and on skew translation generalized quadrangles.