Translation generalized quadrangles / J.A. Thas, K. Thas, H. Van Maldeghem.

Format:

Book

Author/Creator:

Thas, J. A. (Joseph Adolf)

Contributor:

Maldeghem, H. van.

Thas, Koen, 1977-

Series:

Series in pure mathematics ; v. 26.

Series in pure mathematics ; v. 26

Language:

English

Subjects (All):

Finite generalized quadrangles.

Finite geometries.

Physical Description:

1 online resource (376 p.)

Edition:

1st ed.

Place of Publication:

Hackensack, NJ : World Scientific, c2006.

Language Note:

English

Summary:

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. <i>Translation Generalized Qu

Contents:

Contents ; Preface ; Foreword ; 1 Generalized Quadrangles ; 1.1 Finite Generalized Quadrangles ; 1.2 Automorphisms ; 1.3 Grids and Dual Grids ; 1.4 The Classical Generalized Quadrangles ; 1.5 The Generalized Quadrangles T2(O) and T3(O) of Tits

1.6 The Generalized Quadrangles T2(0) 1.7 Orders of the Known Generalized Quadrangles ; 1.8 Generalized Quadrangles with Small Parameters ; 2 Regularity Antiregularity and 3-Regularity ; 2.1 Regularity ; 2.2 Regularity and Dual Nets ; 2.3 Antiregularity

2.4 Antiregularity and Laguerre Planes 2.5 3-Regularity ; 2.6 3-Regularity and Subquadrangles ; 2.7 3-Regularity Inversive Planes and Characterizations ; 3 Elation and Translation Generalized Quadrangles ; 3.1 Some Notions from Group Theory ; 3.2 Elation Generalized Quadrangles

3.3 Translation Generalized Quadrangles 3.4 The Kernel of a Translation Generalized Quadrangle ; 3.5 T(n, m, q)s and Translation Generalized Quadrangles; 3.6 Regular Pseudo-Ovals and Regular Pseudo-Ovoids ; 3.7 Automorphisms of Translation Generalized Quadrangles ; 3.8 Important Properties of O(n, m, q); 3.9 Pseudo-Ovals ; 3.10 Eggs

3.11 The Stabilizer of the Base-Point of a Translation Generalized Quadrangle 3.12 Structure of the Automorphism Group of a Translation Quadrangle ; 4 Generalized Quadrangles and Flocks ; 4.1 Flocks ; 4.2 Flocks and Translation Planes ; 4.3 Flocks of Ovoids and Hyperbolic Quadrics

4.4 Flocks of Cones

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 325-336) and index.

ISBN:

9786611924515

9781281924513

1281924512

9789812772916

981277291X

OCLC:

879023687