Subquadrangles of order \(s\) of generalized quadrangles of order (\(s,s^{2}\)). I
The authors investigate subquadrangles of order \(s\) in generalized quadrangles of order \((s,s^2)\), \(s\) even. The case of odd \(s\) is considered in [J. Comb. Theory, Ser. A, 106, No. 1, 33--48 (2004; see the review below)]. In the present paper, the authors obtain a new characterization result for \(Q(5,s)\), \(s\) even or odd, and use this to complete the classification of the subquadrangles of order \(s\) in dual flock GQ's of order \((s,s^2)\), \(s\) even. They also show that if \(Q\) is a subquadrangle of order \(s\) in a nonclassical translation generalized quadrangle (TGQ) of order \((s,s^2)\), \(s\) even, such that the corresponding egg is good at an element, then \(Q\) necessarily contains the base point of the TGQ.
scientific article; zbMATH DE number 2081937