Finite Generalized Quadrangles

Author : Stanley E. Payne,Joseph Adolf Thas
Publisher : European Mathematical Society
Page : 304 pages
File Size : 41,7 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 : Koen Thas
Publisher : Springer Science & Business Media
Page : 246 pages
File Size : 43,9 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 : Joseph Adolf Thas,Koen Thas,H. van Maldeghem
Publisher : World Scientific
Page : 377 pages
File Size : 43,5 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 : Koen Thas
Publisher : European Mathematical Society
Page : 136 pages
File Size : 55,6 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 : Joseph A Thas,Koen Thas,Hendrik Van Maldeghem
Publisher : World Scientific
Page : 377 pages
File Size : 50,6 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.

Author : Alexander Hulpke,Robert Liebler,Tim Penttila,Akos Seress
Publisher : Walter de Gruyter
Page : 287 pages
File Size : 48,7 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 : Johnson
Publisher : CRC Press
Page : 476 pages
File Size : 49,9 Mb
Release : 1983-01-18
Category : Mathematics
ISBN : 0824710525

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Finite Geometries by Johnson Pdf

Author : Dieter Jungnickel
Publisher : Springer Science & Business Media
Page : 242 pages
File Size : 47,9 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 : 47,6 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 : James Hirschfeld,Joseph A. Thas
Publisher : Springer
Page : 409 pages
File Size : 42,5 Mb
Release : 2016-02-03
Category : Mathematics
ISBN : 9781447167907

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General Galois Geometries by James Hirschfeld,Joseph A. Thas Pdf

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.

Author : Aart Blokhuis,James W.P. Hirschfeld,Dieter Jungnickel,Joseph A. Thas
Publisher : Springer Science & Business Media
Page : 366 pages
File Size : 55,6 Mb
Release : 2013-12-01
Category : Computers
ISBN : 9781461302834

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Finite Geometries by Aart Blokhuis,James W.P. Hirschfeld,Dieter Jungnickel,Joseph A. Thas Pdf

When? These are the proceedings of Finite Geometries, the Fourth Isle of Thorns Conference, which took place from Sunday 16 to Friday 21 July, 2000. It was organised by the editors of this volume. The Third Conference in 1990 was published as Advances in Finite Geometries and Designs by Oxford University Press and the Second Conference in 1980 was published as Finite Geometries and Designs by Cambridge University Press. The main speakers were A. R. Calderbank, P. J. Cameron, C. E. Praeger, B. Schmidt, H. Van Maldeghem. There were 64 participants and 42 contributions, all listed at the end of the volume. Conference web site http://www. maths. susx. ac. uk/Staff/JWPH/ Why? This collection of 21 articles describes the latest research and current state of the art in the following inter-linked areas: • combinatorial structures in finite projective and affine spaces, also known as Galois geometries, in which combinatorial objects such as blocking sets, spreads and partial spreads, ovoids, arcs and caps, as well as curves and hypersurfaces, are all of interest; • geometric and algebraic coding theory; • finite groups and incidence geometries, as in polar spaces, gener alized polygons and diagram geometries; • algebraic and geometric design theory, in particular designs which have interesting symmetric properties and difference sets, which play an important role, because of their close connections to both Galois geometry and coding theory.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 40,7 Mb
Release : 2024-06-03
Category : Electronic
ISBN : 9789814467858

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Perspectives in Mathematical Sciences II by Anonim Pdf

Author : A. Barlotti,A. Bichara,P.V. Ceccherini,G. Tallini
Publisher : Elsevier
Page : 565 pages
File Size : 49,6 Mb
Release : 1992-08-17
Category : Mathematics
ISBN : 0080867928

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Combinatorics '90 by A. Barlotti,A. Bichara,P.V. Ceccherini,G. Tallini Pdf

This volume forms a valuable source of information on recent developments in research in combinatorics, with special regard to the geometric point of view. Topics covered include: finite geometries (arcs, caps, special varieties in a Galois space; generalized quadrangles; Benz planes; foundation of geometry), partial geometries, Buekenhout geometries, transitive permutation sets, flat-transitive geometries, design theory, finite groups, near-rings and semifields, MV-algebras, coding theory, cryptography and graph theory in its geometric and design aspects.

Author : Lino Di Martino,William Kantor,Guglielmo Lunardon,Antonio Pasini,Maria Clara Tamburini
Publisher : Birkhäuser
Page : 267 pages
File Size : 40,9 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 : Library of Congress
Publisher : Unknown
Page : 1704 pages
File Size : 46,5 Mb
Release : 2009
Category : Subject headings, Library of Congress
ISBN : WISC:89104096649

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Library of Congress Subject Headings by Library of Congress Pdf