An Inequality for Generalized Quadrangles

An Integer Sequence Motivated by Generalized Quadrangles

In this paper, we prove a closed form for a sequence motivated by the search for new generalized quadrangles of odd order. We present two proofs: a direct proof to explain the closed form’s derivation and a shorter inductive argument. The sequence in question is derived from congruences that arise from applying the Hermite-Dickson criterion to a permutation polynomial that is related to the gir...

Generalized Quadrangles with an Abelian Singer Group

In this note we characterize thick finite generalized quadrangles constructed from a generalized hyperoval as those admitting an abelian Singer group, i.e., an abelian group acting regularly on the points.

Finite Generalized Quadrangles

Characterizations of Generalized Quadrangles by Generalized Homologies

Let S= (P, B, I) be a generalized quadrangle of order (s, t). For X, y E P, X+ y. let X(x, y) be the group of all collineations of S fixing x and y linewise. If ZE (4 YJL> then the set of all points incident with the line xz (resp. y;) is denoted by z(resp. 3. The generalized quadrangle S = (P, B, I) is said to be (x, y)-transitive, x+ y, if X(x, y) is transitive on each set Z{x, z} and jZ’-{ y...

Moufang-like conditions for generalized quadrangles and classification of all finite quasi-transitive generalized quadrangles

We tell the history ofMoufang generalized quadrangles.We review someMoufang-like conditions, and classify finite quasi-transitive generalized quadrangles. These are generalized quadrangles so that for any two non-concurrent linesU,V of theGQ, and for someW ∈ {U,V }⊥, the group of generalized homologies with axes U and V acts transitively on the points ofW incident with neither U nor V. As a by-...