Finite Generalized Quadrangles
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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.
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 ?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.
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 Abelian p-groups 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.
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.
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.
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.
Q Clan Geometries In Characteristic 2
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Author : Ilaria Cardinali
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-03
Q Clan Geometries In Characteristic 2 written by Ilaria Cardinali 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 2008-01-03 with Mathematics categories.
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.
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.
Generalized Polygons
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Author : Hendrik,van Maldeghem
language : en
Publisher: Birkhäuser
Release Date : 2013-11-09
Generalized Polygons written by Hendrik,van Maldeghem and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-09 with Mathematics categories.
This book is intended to be an introduction to the fascinating theory ofgeneralized polygons for both the graduate student and the specialized researcher in the field. It gathers together a lot of basic properties (some of which are usually referred to in research papers as belonging to folklore) and very recent and sometimes deep results. I have chosen a fairly strict geometrical approach, which requires some knowledge of basic projective geometry. Yet, it enables one to prove some typically group-theoretical results such as the determination of the automorphism groups of certain Moufang polygons. As such, some basic group-theoretical knowledge is required of the reader. The notion of a generalized polygon is a relatively recent one. But it is one of the most important concepts in incidence geometry. Generalized polygons are the building bricks of Tits buildings. They are the prototypes and precursors of more general geometries such as partial geometries, partial quadrangles, semi-partial ge ometries, near polygons, Moore geometries, etc. The main examples of generalized polygons are the natural geometries associated with groups of Lie type of relative rank 2. This is where group theory comes in and we come to the historical raison d'etre of generalized polygons. In 1959 Jacques Tits discovered the simple groups of type 3D by classifying the 4 trialities with at least one absolute point of a D -geometry. The method was 4 predominantly geometric, and so not surprisingly the corresponding geometries (the twisted triality hexagons) came into play. Generalized hexagons were born.
Designs And Finite Geometries
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Author : Dieter Jungnickel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Designs And Finite Geometries written by Dieter Jungnickel 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 2012-12-06 with Mathematics categories.
Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.