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Q-Clan Geometries in Characteristic 2 (Frontiers in Mathematics)

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Q-Clan Geometries in Characteristic 2 (Frontiers in Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

This monograph offers the only comprehensive, coherent treatment of the theory - in characteristic 2 - of the so-called flock quadrangles, i.e., those generalized quadrangles (GQ) that arise from q-clans, along with their associated ovals. Special attention is given to the determination of the complete oval stabilizers of each of the ovals associated with a flock GQ. A concise but logically complete introduction to the basic ideas is given. The theory of these flock GQ has evolved over the past two decades and has reached a level of maturation that makes it possible for the first time to give a satisfactory, unified treatment of all the known examples. The book will be a useful resource for all researchers working in the field of finite geometry, especially those interested in finite generalized quadrangles. It is of particular interest to those studying ovals in finite Desarguesian planes.  

Synopsis:

This book offers a complete proof of the Fundamental Theorem of q-Clan Geometry, followed by a detailed study of the known examples. It completely works out the collineation groups of the associated generalized quadrangles and the stabilizers of their associated ovals.

Synopsis:

A q-clan with q a power of 2 is equivalent to a certain generalized quadrangle with a family of subquadrangles each associated with an oval in the Desarguesian plane of order 2. It is also equivalent to a flock of a quadratic cone, and hence to a line-spread of 3-dimensional projective space and thus to a translation plane, and more. These geometric objects are tied together by the so-called Fundamental Theorem of q-Clan Geometry. The book gives a complete proof of this theorem, followed by a detailed study of the known examples. The collineation groups of the associated generalized quadrangles and the stabilizers of their associated ovals are worked out completely.

Table of Contents

Introduction.- 1. q-Clans and Their Geometries.- 2. The Fundamental Theorem.- 3. Aut(GQ(C)).- 4. The Cyclic q-Clans.- 5. Applications to the Known Cyclis q-Clans.- 6. The Subiaco Oval Stabilizers.- 7. The Adelaide Oval Stabilizers.- 8. The Payne q-Clans.- 9. Other Good Stuff.- Bibliography.

Product Details

ISBN:
9783764385071
Author:
Cardinali, Ilaria
Publisher:
Birkhauser Basel
Author:
Payne, Stanley E.
Author:
Stanle
Author:
y E. Payne
Subject:
Automorphisms.
Subject:
Finite generalized quadrangles.
Subject:
Geometry - General
Subject:
Mathematics-Geometry and Trigonometry
Subject:
Geometry, analytic
Subject:
automorphism group
Subject:
Discrete geometry
Subject:
Quadrangle
Subject:
Convex and Discrete Geometry
Copyright:
Edition Description:
Book
Series:
Frontiers in Mathematics
Publication Date:
20071004
Binding:
TRADE PAPER
Language:
English
Illustrations:
Y
Pages:
180
Dimensions:
240 x 170 mm

Related Subjects

Science and Mathematics » Mathematics » Combinatorics
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Geometry » Algebraic Geometry
Science and Mathematics » Mathematics » Geometry » General
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry

Q-Clan Geometries in Characteristic 2 (Frontiers in Mathematics) Used Trade Paper
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Product details 180 pages Birkhauser Basel - English 9783764385071 Reviews:
"Synopsis" by , This book offers a complete proof of the Fundamental Theorem of q-Clan Geometry, followed by a detailed study of the known examples. It completely works out the collineation groups of the associated generalized quadrangles and the stabilizers of their associated ovals.
"Synopsis" by , A q-clan with q a power of 2 is equivalent to a certain generalized quadrangle with a family of subquadrangles each associated with an oval in the Desarguesian plane of order 2. It is also equivalent to a flock of a quadratic cone, and hence to a line-spread of 3-dimensional projective space and thus to a translation plane, and more. These geometric objects are tied together by the so-called Fundamental Theorem of q-Clan Geometry. The book gives a complete proof of this theorem, followed by a detailed study of the known examples. The collineation groups of the associated generalized quadrangles and the stabilizers of their associated ovals are worked out completely.
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