A Course On Elation Quadrangles

Author : Koen Thas
Publisher : European Mathematical Society
Page : 136 pages
File Size : 49,9 Mb
Release : 2012
Category : Abelian p-groups
ISBN : 3037191104

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A Course on Elation Quadrangles by Koen Thas Pdf

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.

Author : N.S. Narasimha Sastry
Publisher : Springer Science & Business Media
Page : 311 pages
File Size : 51,6 Mb
Release : 2014-04-02
Category : Mathematics
ISBN : 9788132218142

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Groups of Exceptional Type, Coxeter Groups and Related Geometries by N.S. Narasimha Sastry Pdf

The book deals with fundamental structural aspects of algebraic and simple groups, Coxeter groups and the related geometries and buildings. All contributing authors are very active researchers in the topics related to the theme of the book. Some of the articles provide the latest developments in the subject; some provide an overview of the current status of some important problems in this area; some survey an area highlighting the current developments; and some provide an exposition of an area to collect problems and conjectures. It is hoped that these articles would be helpful to a beginner to start independent research on any of these topics, as well as to an expert to know some of the latest developments or to consider some problems for investigation.

Author : Joseph Adolf Thas,Koen Thas,H. van Maldeghem
Publisher : World Scientific
Page : 377 pages
File Size : 48,6 Mb
Release : 2006
Category : Mathematics
ISBN : 9789812569516

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Translation Generalized Quadrangles by Joseph Adolf Thas,Koen Thas,H. van Maldeghem Pdf

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.

Author : Robin Chapman
Publisher : Cambridge University Press
Page : 447 pages
File Size : 51,7 Mb
Release : 2011-06-23
Category : Mathematics
ISBN : 9781139503686

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Surveys in Combinatorics 2011 by Robin Chapman Pdf

This volume contains articles based on the invited lectures given at the 23rd British Combinatorial Conference, held in July 2011 at the University of Exeter. Each article surveys an area of current research in combinatorial mathematics and will be invaluable to anyone wishing to keep abreast of modern developments.

Author : Koen Thas
Publisher : Springer Science & Business Media
Page : 246 pages
File Size : 44,8 Mb
Release : 2004-01-26
Category : Mathematics
ISBN : 3764361581

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Symmetry in Finite Generalized Quadrangles by Koen Thas Pdf

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.

Author : Dieter Jungnickel
Publisher : Springer Science & Business Media
Page : 242 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461313953

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Designs and Finite Geometries by Dieter Jungnickel Pdf

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.

Author : Hendrik Van Maldeghem
Publisher : Springer Science & Business Media
Page : 510 pages
File Size : 43,5 Mb
Release : 2012-01-05
Category : Mathematics
ISBN : 9783034802703

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Generalized Polygons by Hendrik Van Maldeghem Pdf

Generalized Polygons is the first book to cover, in a coherent manner, the theory of polygons from scratch. In particular, it fills elementary gaps in the literature and gives an up-to-date account of current research in this area, including most proofs, which are often unified and streamlined in comparison to the versions generally known. Generalized Polygons will be welcomed both by the student seeking an introduction to the subject as well as the researcher who will value the work as a reference. In particular, it will be of great value for specialists working in the field of generalized polygons (which are, incidentally, the rank 2 Tits-buildings) or in fields directly related to Tits-buildings, incidence geometry and finite geometry. The approach taken in the book is of geometric nature, but algebraic results are included and proven (in a geometric way!). A noteworthy feature is that the book unifies and generalizes notions, definitions and results that exist for quadrangles, hexagons, octagons - in the literature very often considered separately - to polygons. Many alternative viewpoints given in the book heighten the sense of beauty of the subject and help to provide further insight into the matter.​

Author : Anonim
Publisher : Unknown
Page : 490 pages
File Size : 50,9 Mb
Release : 2005
Category : Mathematics
ISBN : UOM:39015058988208

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Bulletin of the Belgian Mathematical Society, Simon Stevin by Anonim Pdf

Author : Alexander Hulpke,Robert Liebler,Tim Penttila,Akos Seress
Publisher : Walter de Gruyter
Page : 287 pages
File Size : 51,6 Mb
Release : 2008-08-22
Category : Mathematics
ISBN : 9783110199741

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Finite Geometries, Groups, and Computation by Alexander Hulpke,Robert Liebler,Tim Penttila,Akos Seress Pdf

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.

Author : Stanley E. Payne,Joseph Adolf Thas
Publisher : European Mathematical Society
Page : 304 pages
File Size : 43,5 Mb
Release : 2009
Category : Mathematics
ISBN : 3037190663

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Finite Generalized Quadrangles by Stanley E. Payne,Joseph Adolf Thas Pdf

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.

Author : Lino Di Martino,William Kantor,Guglielmo Lunardon,Antonio Pasini,Maria Clara Tamburini
Publisher : Birkhäuser
Page : 267 pages
File Size : 50,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783034888196

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Groups and Geometries by Lino Di Martino,William Kantor,Guglielmo Lunardon,Antonio Pasini,Maria Clara Tamburini Pdf

On September 1-7, 1996 a conference on Groups and Geometries took place in lovely Siena, Italy. It brought together experts and interested mathematicians from numerous countries. The scientific program centered around invited exposi tory lectures; there also were shorter research announcements, including talks by younger researchers. The conference concerned a broad range of topics in group theory and geometry, with emphasis on recent results and open problems. Special attention was drawn to the interplay between group-theoretic methods and geometric and combinatorial ones. Expanded versions of many of the talks appear in these Proceedings. This volume is intended to provide a stimulating collection of themes for a broad range of algebraists and geometers. Among those themes, represented within the conference or these Proceedings, are aspects of the following: 1. the classification of finite simple groups, 2. the structure and properties of groups of Lie type over finite and algebraically closed fields of finite characteristic, 3. buildings, and the geometry of projective and polar spaces, and 4. geometries of sporadic simple groups. We are grateful to the authors for their efforts in providing us with manuscripts in LaTeX. Barbara Priwitzer and Thomas Hintermann, Mathematics Editors of Birkhauser, have been very helpful and supportive throughout the preparation of this volume.

Author : Judith N. Cederberg
Publisher : Springer Science & Business Media
Page : 456 pages
File Size : 53,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475734904

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A Course in Modern Geometries by Judith N. Cederberg Pdf

Designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school. The first chapter presents several finite geometries in an axiomatic framework, while Chapter 2 continues the synthetic approach in introducing both Euclids and ideas of non-Euclidean geometry. There follows a new introduction to symmetry and hands-on explorations of isometries that precedes an extensive analytic treatment of similarities and affinities. Chapter 4 presents plane projective geometry both synthetically and analytically, and the new Chapter 5 uses a descriptive and exploratory approach to introduce chaos theory and fractal geometry, stressing the self-similarity of fractals and their generation by transformations from Chapter 3. Throughout, each chapter includes a list of suggested resources for applications or related topics in areas such as art and history, plus this second edition points to Web locations of author-developed guides for dynamic software explorations of the Poincaré model, isometries, projectivities, conics and fractals. Parallel versions are available for "Cabri Geometry" and "Geometers Sketchpad".

Author : Anonim
Publisher : Unknown
Page : 840 pages
File Size : 46,5 Mb
Release : 2007
Category : Mathematics
ISBN : UOM:39015078588582

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Mathematical Reviews by Anonim Pdf

Author : Judith Cederberg
Publisher : Springer
Page : 254 pages
File Size : 44,5 Mb
Release : 1989
Category : Mathematics
ISBN : UOM:39076000911177

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A Course in Modern Geometries by Judith Cederberg Pdf

A Course in Modern Geometries is designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school. Chapter 1 presents several finite geometries in an axiomatic framework. Chapter 2 introduces Euclid's geometry and the basic ideas of non-Euclidean geometry. The synthetic approach of Chapters 1 - 2 is followed by the analytic treatment of transformations of the Euclidean plane in Chapter 3. Chapter 4 presents plane projective geometry both synthetically and analytically. The extensive use of matrix representations of groups of transformations in Chapters 3 - 4 reinforces ideas from linear algebra and serves as excellent preparation for a course in abstract algebra. Each chapter includes a list of suggested sources for applications and/or related topics.

Author : Joseph A Thas,Koen Thas,Hendrik Van Maldeghem
Publisher : World Scientific
Page : 377 pages
File Size : 49,9 Mb
Release : 2006-09-28
Category : Mathematics
ISBN : 9789814477284

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Translation Generalized Quadrangles by Joseph A Thas,Koen Thas,Hendrik Van Maldeghem Pdf

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.