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Translation Generalized Quadrangles

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Translation Generalized Quadrangles

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Author : Joseph Adolf Thas
language : en
Publisher: World Scientific
Release Date : 2006

Translation Generalized Quadrangles written by Joseph Adolf Thas and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

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 OC Moufang ConditionOCO, 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: OC Finite Generalized QuadranglesOCO (1984) by S E Payne and J A Thas, OC Generalized PolygonsOCO (1998) by H Van Maldeghem, and OC Symmetry in Finite Generalized QuadranglesOCO (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.

Translation Generalized Quadrangles

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Author : Joseph A Thas
language : en
Publisher: World Scientific
Release Date : 2006-09-28

Translation Generalized Quadrangles written by Joseph A Thas and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-28 with Mathematics categories.

Finite Generalized Quadrangles

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Author : Stanley E. Payne
language : en
Publisher: European Mathematical Society
Release Date : 2009

Finite Generalized Quadrangles written by Stanley E. Payne and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

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.

Symmetry In Finite Generalized Quadrangles

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Author : Koen Thas
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-01-26

Symmetry In Finite Generalized Quadrangles written by Koen Thas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-26 with Mathematics categories.

This monograph classifies finite generalized quadrangles by symmetry, generalizing the celebrated Lenz-Barlotti classification for projective planes. The book introduces combinatorial, geometrical and group-theoretical concepts that arise in the classification and in the general theory of finite generalized quadrangles, including automorphism groups, elation and translation generalized quadrangles, generalized ovals and generalized ovoids, span-symmetric generalized quadrangles, flock geometry and property (G), regularity and nets, split BN-pairs of rank 1, and the Moufang property.

A Course On Elation Quadrangles

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Author : Koen Thas
language : en
Publisher: European Mathematical Society
Release Date : 2012

A Course On Elation Quadrangles written by Koen Thas and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

The notion of elation generalized quadrangle is a natural generalization to the theory of generalized quadrangles of the important notion of translation planes in the theory of projective planes. Almost any known class of finite generalized quadrangles can be constructed from a suitable class of elation quadrangles. In this book the author considers several aspects of the theory of elation generalized quadrangles. Special attention is given to local Moufang conditions on the foundational level, exploring, for instance, Knarr's question from the 1990s concerning the very notion of elation quadrangles. All the known results on Kantor's prime power conjecture for finite elation quadrangles are gathered, some of them published here for the first time. The structural theory of elation quadrangles and their groups is heavily emphasized. Other related topics, such as $p$-modular cohomology, Heisenberg groups, and existence problems for certain translation nets, are briefly touched. This book starts from scratch and is essentially self-contained. Many alternative proofs are given for known theorems. This course contains dozens of exercises at various levels, from very easy to rather difficult, and will stimulate undergraduate and graduate students to enter the fascinating and rich world of elation quadrangles. More accomplished mathematicians will find the final chapters especially challenging.

General Galois Geometries

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Author : James Hirschfeld
language : en
Publisher: Springer
Release Date : 2016-02-03

General Galois Geometries written by James Hirschfeld and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-03 with Mathematics categories.

This book is the second edition of the third and last volume of a treatise on projective spaces over a finite field, also known as Galois geometries. This volume completes the trilogy comprised of plane case (first volume) and three dimensions (second volume). This revised edition includes much updating and new material. It is a mostly self-contained study of classical varieties over a finite field, related incidence structures and particular point sets in finite n-dimensional projective spaces. General Galois Geometries is suitable for PhD students and researchers in combinatorics and geometry. The separate chapters can be used for courses at postgraduate level.

Finite Geometries Groups And Computation

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Author : Alexander Hulpke
language : en
Publisher: Walter de Gruyter
Release Date : 2008-08-22

Finite Geometries Groups And Computation written by Alexander Hulpke and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-22 with Mathematics categories.

This volume is the proceedings of a conference on Finite Geometries, Groups, and Computation that took place on September 4-9, 2004, at Pingree Park, Colorado (a campus of Colorado State University). Not accidentally, the conference coincided with the 60th birthday of William Kantor, and the topics relate to his major research areas. Participants were encouraged to explore the deeper interplay between these fields. The survey papers by Kantor, O'Brien, and Penttila should serve to introduce both students and the broader mathematical community to these important topics and some of their connections while the volume as a whole gives an overview of current developments in these fields.

Finite Geometries

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Author : Johnson
language : en
Publisher: CRC Press
Release Date : 1983-01-18

Finite Geometries written by Johnson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-01-18 with Mathematics categories.

Perspectives In Mathematical Science Ii Pure Mathematics

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Author : N S Narasimha Sastry
language : en
Publisher: World Scientific
Release Date : 2009-07-01

Perspectives In Mathematical Science Ii Pure Mathematics written by N S Narasimha Sastry and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-01 with Mathematics categories.

This book presents a collection of invited articles by distinguished Mathematicians on the occasion of the Platinum Jubilee Celebrations of the Indian Statistical Institute, during the year 2007. These articles provide a current perspective of different areas of research, emphasizing the major challenging issues. Given the very significant record of the Institute in research in the areas of Statistics, Probability and Mathematics, distinguished authors have very admirably responded to the invitation. Some of the articles are written keeping students and potential new entrants to an area of mathematics in mind. This volume is thus very unique and gives a perspective of several important aspects of mathematics.

Points And Lines

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Author : Ernest E. Shult
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-12-13

Points And Lines written by Ernest E. Shult and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-13 with Mathematics categories.

The classical geometries of points and lines include not only the projective and polar spaces, but similar truncations of geometries naturally arising from the groups of Lie type. Virtually all of these geometries (or homomorphic images of them) are characterized in this book by simple local axioms on points and lines. Simple point-line characterizations of Lie incidence geometries allow one to recognize Lie incidence geometries and their automorphism groups. These tools could be useful in shortening the enormously lengthy classification of finite simple groups. Similarly, recognizing ruled manifolds by axioms on light trajectories offers a way for a physicist to recognize the action of a Lie group in a context where it is not clear what Hamiltonians or Casimir operators are involved. The presentation is self-contained in the sense that proofs proceed step-by-step from elementary first principals without further appeal to outside results. Several chapters have new heretofore unpublished research results. On the other hand, certain groups of chapters would make good graduate courses. All but one chapter provide exercises for either use in such a course, or to elicit new research directions.

Translation Generalized Quadrangles

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