Thas J.A., Thas K., Van Maldeghem H. Translation Generalized Quadrangles

World Scientific Publishing, 2006. — 377 p. — (Series in Pure Mathematics 26). — ISBN 981-256-951-0.Translation generalized quadrangles play a key role in the theory of generalized quadrangles, comparable to the role of translation planes in the theory of projective and affine planes. The notion of translation generalized quadrangle is a local analog of the more global "Moufang Condition", a topic of great interest, also due to the classification of all Moufang polygons. Attention is thus paid to recent results in that direction, but also many of the most important results in the general theory of generalized quadrangles that appeared since 1984 are treated.Generalized Quadrangles
Regularity, Antiregularity and 3-Regularity
Elation and Translation Generalized Quadrangles
Generalized Quadrangles and Flocks
Good Eggs
Generalized Quadrangles, Nets and the Axiom of Veblen
Ovoids and Subquadrangles
Translation Generalized Ovals
Moufang Sets and Translation Moufang Sets
Configurations of Translation Points
Moufang Quadrangles with a Translation Point
Translation Ovoids in Translation Quadrangles
Translation Generalized Quadrangles in Projective Space
Open Problems