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Finite Generalized Quadrangles: Second Edition
Stanley E. Payne, University of Colorado, Denver, CO, and Joseph A. Thas, Ghent University, Belgium
A publication of the European Mathematical Society.
EMS Series of Lectures in Mathematics
2009; 298 pp; softcover
Volume: 9
ISBN-10: 3-03719-066-3
ISBN-13: 978-3-03719-066-1
List Price: US$58
Member Price: US$46.40
Order Code: EMSSERLEC/9
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Generalized quadrangles (GQ) were formally introduced by J. Tits in 1959 to describe geometric properties of simple groups of Lie type of rank 2. The first edition of Finite Generalized Quadrangles (FGQ) quickly became the standard reference for finite GQ.

The second edition is essentially a reprint of the first edition. It is a careful rendering into LaTeX of the original, along with an appendix that brings to the attention of the reader those major new results pertaining to GQ, especially in those areas where the authors of this work have made a contribution.

The first edition has been out of print for many years. The new edition makes available again this classical reference in the rapidly increasing field of finite geometries.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.


Graduate students and research mathematicians interested in generalized quadrangles.

Table of Contents

  • Combinatorics of finite generalized quadrangles
  • Subquadrangles
  • The known generalized quadrangles and their properties
  • Generalized quadrangles in finite projective spaces
  • Combinatorial characterizations of the known generalized quadrangles
  • Generalized quadrangles with small parameters
  • Generalized quadrangles in finite affine spaces
  • Elation generalized quadrangles and translation generalized quadrangles
  • Moufang conditions
  • Generalized quadrangles as group coset geometries
  • Coordinatization of generalized quadrangles with \(s=t\)
  • Generalized quadrangles as amalgamations of desarguesian planes
  • Generalizations and related topics
  • Appendix. Development of the theory of GQ since 1983
  • Bibliography
  • Index
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