Groups Combinatorics Geometry

Author by : A. A. Ivanov
Languange : en
Publisher by : World Scientific
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Description : Over the past 20 years, the theory of groups in particular simplegroups, finite and algebraic has influenced a number of diverseareas of mathematics. Such areas include topics where groups have beentraditionally applied, such as algebraic combinatorics, finitegeometries, Galois theory and permutation groups, as well as severalmore recent developments.


Groups Combinatorics Geometry

Author by : A. A. Ivanov
Languange : en
Publisher by : World Scientific
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Total Read : 99
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Description : "This book contains the proceedings of the L.M.S. Durham Symposium on Groups, Geometry and Combinatorics, July 16-26, 2001"--P. v.


Infinite Groups Geometric Combinatorial And Dynamical Aspects

Author by : Laurent Bartholdi
Languange : en
Publisher by : Springer Science & Business Media
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Total Read : 73
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Description : This book offers a panorama of recent advances in the theory of infinite groups. It contains survey papers contributed by leading specialists in group theory and other areas of mathematics. Topics include amenable groups, Kaehler groups, automorphism groups of rooted trees, rigidity, C*-algebras, random walks on groups, pro-p groups, Burnside groups, parafree groups, and Fuchsian groups. The accent is put on strong connections between group theory and other areas of mathematics.


Groups Combinatorics And Geometry

Author by : A A Ivanov
Languange : en
Publisher by : World Scientific
Format Available : PDF, ePub, Mobi
Total Read : 48
Total Download : 413
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Description : Over the past 20 years, the theory of groups — in particular simple groups, finite and algebraic — has influenced a number of diverse areas of mathematics. Such areas include topics where groups have been traditionally applied, such as algebraic combinatorics, finite geometries, Galois theory and permutation groups, as well as several more recent developments. Among the latter are probabilistic and computational group theory, the theory of algebraic groups over number fields, and model theory, in each of which there has been a major recent impetus provided by simple group theory. In addition, there is still great interest in local analysis in finite groups, with substantial new input from methods of geometry and amalgams, and particular emphasis on the revision project for the classification of finite simple groups. This important book contains 20 survey articles covering many of the above developments. It should prove invaluable for those working in the theory of groups and its applications. Contents:Curtis–Phan–Tits Theory (C D Bennett et al.)Derangements in Simple and Primitive Groups (J Fulman & R Guralnick)Computing with Matrix Groups (W M Kantor & Á Seress)Bases of Primitive Permutation Groups (M W Liebeck & A Shalev)Modular Subgroup Arithmetic (T W Müller)Counting Nets in the Monster (S P Norton)Overgroups of Finite Quasiprimitive Permutation Groups (C E Praeger)Old Groups Can Learn New Tricks (L Pyber)Structure and Presentations of Lie-Type Groups (F G Timmesfeld)Computing in the Monster (R A Wilson)and other papers Readership: Graduate students, researchers and academics in algebra. Keywords:Simple Groups;Algebraic Combinatorics;Finite Geometry;Permutation Groups. Probabilistic Group


Combinatorial Group Theory And Applications To Geometry

Author by : D.J. Collins
Languange : en
Publisher by : Springer Science & Business Media
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Description : This book consists of two parts. The first part provides a comprehensive description of that part of group theory which has its roots in topology. The second more advanced part deals with recent work on groups relating to topological manifolds. It is a valuable guide to research in this field. The text contains numerous examples, sketches of proofs and open problems.


Algebra Vii

Author by : D.J. Collins
Languange : en
Publisher by : Springer Science & Business Media
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Total Read : 15
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Description : From the reviews: "... The book under review consists of two monographs on geometric aspects of group theory ... Together, these two articles form a wide-ranging survey of combinatorial group theory, with emphasis very much on the geometric roots of the subject. This will be a useful reference work for the expert, as well as providing an overview of the subject for the outsider or novice. Many different topics are described and explored, with the main results presented but not proved. This allows the interested reader to get the flavour of these topics without becoming bogged down in detail. Both articles give comprehensive bibliographies, so that it is possible to use this book as the starting point for a more detailed study of a particular topic of interest. ..." Bulletin of the London Mathematical Society, 1996


Algorithms And Classification In Combinatorial Group Theory

Author by : Gilbert Baumslag
Languange : en
Publisher by : Springer Science & Business Media
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Total Read : 51
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Description : The papers in this volume are the result of a workshop held in January 1989 at the Mathematical Sciences Research Institute. Topics covered include decision problems, finitely presented simple groups, combinatorial geometry and homology, and automatic groups and related topics.


Groups Combinatorics And Geometry

Author by : Martin W. Liebeck
Languange : en
Publisher by : Cambridge University Press
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Description : This volume contains a collection of papers on the subject of the classification of finite simple groups.


Combinatorics Of Coxeter Groups

Author by : Anders Bjorner
Languange : en
Publisher by : Springer Science & Business Media
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Total Read : 23
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Description : Includes a rich variety of exercises to accompany the exposition of Coxeter groups Coxeter groups have already been exposited from algebraic and geometric perspectives, but this book will be presenting the combinatorial aspects of Coxeter groups


Combinatorial And Geometric Group Theory Edinburgh 1993

Author by : Andrew J. Duncan
Languange : en
Publisher by : Cambridge University Press
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Total Read : 9
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Description : Authoritative collection of surveys and papers. Indispensable to all research workers in the area.


Combinatorial And Geometric Group Theory

Author by : Sean Cleary
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 78
Total Download : 777
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Description : This volume grew out of two AMS conferences held at Columbia University (New York, NY) and the Stevens Institute of Technology (Hoboken, NJ) and presents articles on a wide variety of topics in group theory. Readers will find a variety of contributions, including a collection of over 170 open problems in combinatorial group theory, three excellent survey papers (on boundaries of hyperbolic groups, on fixed points of free group automorphisms, and on groups of automorphisms of compact Riemann surfaces), and several original research papers that represent the diversity of current trends in combinatorial and geometric group theory. The book is an excellent reference source for graduate students and research mathematicians interested in various aspects of group theory.


Combinatorial And Geometric Group Theory

Author by : Oleg Bogopolski
Languange : en
Publisher by : Springer Science & Business Media
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Total Read : 52
Total Download : 274
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Description : This volume assembles several research papers in all areas of geometric and combinatorial group theory originated in the recent conferences in Dortmund and Ottawa in 2007. It contains high quality refereed articles developing new aspects of these modern and active fields in mathematics. It is also appropriate to advanced students interested in recent results at a research level.


Combinatorial Geometry With Applications To Field Theory

Author by : Linfan Mao
Languange : en
Publisher by : Infinite Study
Format Available : PDF, ePub, Mobi
Total Read : 66
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Description : This monograph is motivated with surveying mathematics and physics by CC conjecture, i.e., a mathematical science can be reconstructed from or made by combinatorialization. Topics covered in this book include fundamental of mathematical combinatorics, differential Smarandache n-manifolds, combinatorial or differentiable manifolds and submanifolds, Lie multi-groups, combinatorial principal fiber bundles, gravitational field, quantum fields with their combinatorial generalization, also with discussions on fundamental questions in epistemology. All of these are valuable for researchers in combinatorics, topology, differential geometry, gravitational or quantum fields.


Topics In Geometric Group Theory

Author by : Pierre de la Harpe
Languange : en
Publisher by : University of Chicago Press
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Total Read : 98
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Description : In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades. A recognized expert in the field, de la Harpe adopts a hands-on approach, illustrating key concepts with numerous concrete examples. The first five chapters present basic combinatorial and geometric group theory in a unique and refreshing way, with an emphasis on finitely generated versus finitely presented groups. In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the "Grigorchuk group." Most sections are followed by exercises and a list of problems and complements, enhancing the book's value for students; problems range from slightly more difficult exercises to open research problems in the field. An extensive list of references directs readers to more advanced results as well as connections with other fields.


Groups Combinatorics Geometry

Author by : Martin W. Liebeck
Languange : en
Publisher by : Unknown
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Total Read : 90
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Description : Since the classification of finite simple groups was announced in 1980 the subject has continued to expand opening many new areas of research. This volume contains a collection of papers, both survey and research, arising from the 1990 Durham conference in which the excellent progress of the decade was surveyed and new goals considered. The material is divided into eight sections: sporadic groups; moonshine; local and geometric methods in group theory; geometries and related groups; finite and algebraic groups of Lie type; finite permutation groups; further aspects of Lie groups; related topics. The list of contributors is impressive and the subjects covered include many of the fascinating developments in group theory that have occurred in recent years. It will be an invaluable document for mathematicians working in group theory, combinatorics and geometry.


Combinatorial Methods

Author by : Vladimir Shpilrain
Languange : en
Publisher by : Springer Science & Business Media
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Total Read : 64
Total Download : 105
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Description : The main purpose of this book is to show how ideas from combinatorial group theory have spread to two other areas of mathematics: the theory of Lie algebras and affine algebraic geometry. Some of these ideas, in turn, came to combinatorial group theory from low-dimensional topology in the beginning of the 20th Century.


Combinatorial Number Theory And Additive Group Theory

Author by : Alfred Geroldinger
Languange : en
Publisher by : Springer Science & Business Media
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Total Read : 25
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Description : Additive combinatorics is a relatively recent term coined to comprehend the developments of the more classical additive number theory, mainly focussed on problems related to the addition of integers. Some classical problems like the Waring problem on the sum of k-th powers or the Goldbach conjecture are genuine examples of the original questions addressed in the area. One of the features of contemporary additive combinatorics is the interplay of a great variety of mathematical techniques, including combinatorics, harmonic analysis, convex geometry, graph theory, probability theory, algebraic geometry or ergodic theory. This book gathers the contributions of many of the leading researchers in the area and is divided into three parts. The two first parts correspond to the material of the main courses delivered, Additive combinatorics and non-unique factorizations, by Alfred Geroldinger, and Sumsets and structure, by Imre Z. Ruzsa. The third part collects the notes of most of the seminars which accompanied the main courses, and which cover a reasonably large part of the methods, techniques and problems of contemporary additive combinatorics.


Geometry And Combinatorics

Author by : J. J. Seidel
Languange : en
Publisher by : Academic Press
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Total Read : 20
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Description : Geometry and Combinatorics: Selected Works of J. J. Seidel brings together some of the works of J. J. Seidel in geometry and combinatorics. Seidel's selected papers are divided into four areas: graphs and designs; lines with few angles; matrices and forms; and non-Euclidean geometry. A list of all of Seidel's publications is included. Comprised of 29 chapters, this book begins with a discussion on equilateral point sets in elliptic geometry, followed by an analysis of strongly regular graphs of L2-type and of triangular type. The reader is then introduced to strongly regular graphs with (-1, 1, 0) adjacency matrix having eigenvalue 3; graphs related to exceptional root systems; and equiangular lines. Subsequent chapters deal with the regular two-graph on 276 vertices; the congruence order of the elliptic plane; equi-isoclinic subspaces of Euclidean spaces; and Wielandt's visibility theorem. This monograph will be of interest to students and practitioners in the field of mathematics.


Geometric Group Theory

Author by : Clara Löh
Languange : en
Publisher by : Springer
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Total Read : 26
Total Download : 237
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Description : Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.


Two Dimensional Homotopy And Combinatorial Group Theory

Author by : Cynthia Hog-Angeloni
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 26
Total Download : 874
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Description : This book considers the current state of knowledge in the geometric and algebraic aspects of two-dimensional homotopy theory.


Discrete Geometry And Symmetry

Author by : Marston D. E. Conder
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 67
Total Download : 879
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Description : This book consists of contributions from experts, presenting a fruitful interplay between different approaches to discrete geometry. Most of the chapters were collected at the conference “Geometry and Symmetry” in Veszprém, Hungary from 29 June to 3 July 2015. The conference was dedicated to Károly Bezdek and Egon Schulte on the occasion of their 60th birthdays, acknowledging their highly regarded contributions in these fields. While the classical problems of discrete geometry have a strong connection to geometric analysis, coding theory, symmetry groups, and number theory, their connection to combinatorics and optimization has become of particular importance. The last decades have seen a revival of interest in discrete geometric structures and their symmetry. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory and geometry, combinatorial group theory, and hyperbolic geometry and topology. This book contains papers on new developments in these areas, including convex and abstract polytopes and their recent generalizations, tiling and packing, zonotopes, isoperimetric inequalities, and on the geometric and combinatorial aspects of linear optimization. The book is a valuable resource for researchers, both junior and senior, in the field of discrete geometry, combinatorics, or discrete optimization. Graduate students find state-of-the-art surveys and an open problem collection.


Geometry Combinatorial Designs And Related Structures

Author by : Reader in Mathematics J W P Hirschfeld
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 13
Total Download : 358
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Description : This volume examines state of the art research in finite geometries and designs.


Surveys In Combinatorics 1995

Author by : British Combinatorial Conference
Languange : en
Publisher by : Cambridge University Press
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Total Read : 91
Total Download : 128
File Size : 47,9 Mb
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Description : This volume provides an up-to-date survey of current research activity in several areas of combinatorics and its applications. These include distance-regular graphs, combinatorial designs, coding theory, spectra of graphs, and randomness and computation. The articles give an overview of combinatorics that will be extremely useful to both mathematicians and computer scientists.


Groups Languages And Geometry

Author by : Robert H. Gilman
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 66
Total Download : 939
File Size : 47,7 Mb
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Description : This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Geometric Group Theory and Computer Science held at Mount Holyoke College (South Hadley, MA). The conference was devoted to computational aspects of geometric group theory, a relatively young area of research which has grown out of an influx of ideas from topology and computer science into combinatorial group theory. The book reflects recent progress in this interesting new field. Included are articles about insights from computer experiments, applications of formal language theory, decision problems, and complexity problems. There is also a survey of open questions in combinatorial group theory. The volume will interest group theorists, topologists, and experts in automata and language theory.


Combinatorial Group Theory

Author by : Roger C. Lyndon
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 50
Total Download : 690
File Size : 42,5 Mb
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Description : From the reviews: "This book [...] defines the boundaries of the subject now called combinatorial group theory. [...] it is a considerable achievement to have concentrated a survey of the subject into 339 pages. [...] a valuable and welcome addition to the literature, containing many results not previously available in a book. It will undoubtedly become a standard reference." Mathematical Reviews


Quadratic Forms With Applications To Algebraic Geometry And Topology

Author by : Albrecht Pfister
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 91
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Description : Bringing together thirty years' worth of results about quadratic forms, the topics in this collection include Hilbert's 17th problem, the Tsen-Lang theory of quasi-algebraically closed fields, the level of topological spaces, and systems of quadratic forms over arbitrary fields.