Design theory
Generalized quadrangles of order (s,s2): recent results
Discrete Mathematics
Symmetry in Generalized Quadrangles
Designs, Codes and Cryptography
Journal of Combinatorial Theory Series A
Notes on elation generalized quadrangles
European Journal of Combinatorics
Subquadrangles of order s of generalized quadrangles of order (s, s2), Part I
Journal of Combinatorial Theory Series A
Subquadrangles of order s of generalized quadrangles of order (s, s2), Part II
Journal of Combinatorial Theory Series A
Determination of generalized quadrangles with distinct elation points
Journal of Algebraic Combinatorics: An International Journal
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Suppose \mathcal{S} is a generalized quadrangle (GQ) of order (s, t), s, t \ne 1, with a regular point. Then there is a net which arises from this regular point. We prove 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, and we necessarily have that s = t^2. This result has many applications, of which we give one example. Suppose \mathcal{S} is an elation generalized quadrangle (EGQ) of order (s, t), s, t \ne 1, with elation point p. Then \mathcal{S} is called a skew translation generalized quadrangle (STGQ) with base-point p if there is a full group of symmetries about p of order t which is contained in the elation group. We show that a GQ \mathcal{S} of order s is an STGQ with base-point p if and only if p is an elation point which is regular.