Translation Generalized Quadrangles
Translation Generalized QuadrangleseBook - 2006
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 analogue 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. Translation Generalized Quadrangles is essentially self-contained, as the reader is only expected to be familiar with some basic facts on finite generalized quadrangles. Proofs that are either too long or too technical are left out, or just sketched. The three standard works on generalized quadrangles are (co-)authored by the writers of this book: "Finite Generalized Quadrangles" (1984) by S E Payne and J A Thas, "Generalized Polygons" (1998) by H Van Maldeghem, and "Symmetry in Finite Generalized Quadrangles" (2004) by K Thas. Sample Chapter(s). Chapter 1: Generalized Quadrangles (127 KB). Contents: 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. Readership: Researchers in incidence geometry, combinatorics and finite geometries. Also suitable as a textbook for a graduate course.
Publisher: River Edge : World Scientific Publishing Company, 2006
Copyright Date: ©2006
Branch Call Number: Electronic book
Characteristics: 1 online resource (376 pages)