Orderable Groups

Author : Adam Clay,Dale Rolfsen
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 44,9 Mb
Release : 2016-11-16
Category : Knot theory
ISBN : 9781470431068

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Ordered Groups and Topology by Adam Clay,Dale Rolfsen Pdf

This book deals with the connections between topology and ordered groups. It begins with a self-contained introduction to orderable groups and from there explores the interactions between orderability and objects in low-dimensional topology, such as knot theory, braid groups, and 3-manifolds, as well as groups of homeomorphisms and other topological structures. The book also addresses recent applications of orderability in the studies of codimension-one foliations and Heegaard-Floer homology. The use of topological methods in proving algebraic results is another feature of the book. The book was written to serve both as a textbook for graduate students, containing many exercises, and as a reference for researchers in topology, algebra, and dynamical systems. A basic background in group theory and topology is the only prerequisite for the reader.

Author : Valeriĭ Matveevich Kopytov,V.M. Kopytov,Nikolai Yakovlevich Medvedev
Publisher : Springer Science & Business Media
Page : 268 pages
File Size : 42,6 Mb
Release : 1996-04-30
Category : Mathematics
ISBN : 0306110601

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Right-Ordered Groups by Valeriĭ Matveevich Kopytov,V.M. Kopytov,Nikolai Yakovlevich Medvedev Pdf

The notion of right-ordered groups is fundamental in theories of I-groups, ordered groups, torsion-free groups, and the theory of zero-divisors free rings, as well as in theoretical physics. Right-Ordered Groups is the first book to provide a systematic presentation of right-ordered group theory, describing all known and new results in the field. The volume addresses topics such as right-ordered groups and order permutation groups, the system of convex subgroups of a right-ordered group, and free products of right-ordered groups.

Author : V.M. Kopytov,N.Ya. Medvedev
Publisher : Springer Science & Business Media
Page : 408 pages
File Size : 41,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401583046

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The Theory of Lattice-Ordered Groups by V.M. Kopytov,N.Ya. Medvedev Pdf

A partially ordered group is an algebraic object having the structure of a group and the structure of a partially ordered set which are connected in some natural way. These connections were established in the period between the end of 19th and beginning of 20th century. It was realized that ordered algebraic systems occur in various branches of mathemat ics bound up with its fundamentals. For example, the classification of infinitesimals resulted in discovery of non-archimedean ordered al gebraic systems, the formalization of the notion of real number led to the definition of ordered groups and ordered fields, the construc tion of non-archimedean geometries brought about the investigation of non-archimedean ordered groups and fields. The theory of partially ordered groups was developed by: R. Dedekind, a. Holder, D. Gilbert, B. Neumann, A. I. Mal'cev, P. Hall, G. Birkhoff. These connections between partial order and group operations allow us to investigate the properties of partially ordered groups. For exam ple, partially ordered groups with interpolation property were intro duced in F. Riesz's fundamental paper [1] as a key to his investigations of partially ordered real vector spaces, and the study of ordered vector spaces with interpolation properties were continued by many functional analysts since. The deepest and most developed part of the theory of partially ordered groups is the theory of lattice-ordered groups. In the 40s, following the publications of the works by G. Birkhoff, H. Nakano and P.

Author : M.E Anderson,T.H. Feil
Publisher : Springer Science & Business Media
Page : 197 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9789400928718

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Lattice-Ordered Groups by M.E Anderson,T.H. Feil Pdf

The study of groups equipped with a compatible lattice order ("lattice-ordered groups" or "I!-groups") has arisen in a number of different contexts. Examples of this include the study of ideals and divisibility, dating back to the work of Dedekind and continued by Krull; the pioneering work of Hahn on totally ordered abelian groups; and the work of Kantorovich and other analysts on partially ordered function spaces. After the Second World War, the theory of lattice-ordered groups became a subject of study in its own right, following the publication of fundamental papers by Birkhoff, Nakano and Lorenzen. The theory blossomed under the leadership of Paul Conrad, whose important papers in the 1960s provided the tools for describing the structure for many classes of I!-groups in terms of their convex I!-subgroups. A particularly significant success of this approach was the generalization of Hahn's embedding theorem to the case of abelian lattice-ordered groups, work done with his students John Harvey and Charles Holland. The results of this period are summarized in Conrad's "blue notes" [C].

Author : Andrew Martin William Glass
Publisher : World Scientific
Page : 326 pages
File Size : 52,9 Mb
Release : 1999
Category : Mathematics
ISBN : 9810234937

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Partially Ordered Groups by Andrew Martin William Glass Pdf

"The author's style of writing is very lucid, and the material presented is self-contained. It is an excellent reference text for a graduate course in this area, as well as a source of material for individual reading".Bulletin of London Mathematical Society

Author : Manfred Droste,László Fuchs,Brendan Goldsmith,Lutz Strüngmann
Publisher : Springer
Page : 475 pages
File Size : 45,8 Mb
Release : 2017-06-02
Category : Mathematics
ISBN : 9783319517186

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Groups, Modules, and Model Theory - Surveys and Recent Developments by Manfred Droste,László Fuchs,Brendan Goldsmith,Lutz Strüngmann Pdf

This volume focuses on group theory and model theory with a particular emphasis on the interplay of the two areas. The survey papers provide an overview of the developments across group, module, and model theory while the research papers present the most recent study in those same areas. With introductory sections that make the topics easily accessible to students, the papers in this volume will appeal to beginning graduate students and experienced researchers alike. As a whole, this book offers a cross-section view of the areas in group, module, and model theory, covering topics such as DP-minimal groups, Abelian groups, countable 1-transitive trees, and module approximations. The papers in this book are the proceedings of the conference “New Pathways between Group Theory and Model Theory,” which took place February 1-4, 2016, in Mülheim an der Ruhr, Germany, in honor of the editors’ colleague Rüdiger Göbel. This publication is dedicated to Professor Göbel, who passed away in 2014. He was one of the leading experts in Abelian group theory.

Author : Tullio Ceccherini-Silberstein,Michel Coornaert
Publisher : Springer Nature
Page : 638 pages
File Size : 49,5 Mb
Release : 2023-11-01
Category : Mathematics
ISBN : 9783031103919

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Exercises in Cellular Automata and Groups by Tullio Ceccherini-Silberstein,Michel Coornaert Pdf

This book complements the authors’ monograph Cellular Automata and Groups [CAG] (Springer Monographs in Mathematics). It consists of more than 600 fully solved exercises in symbolic dynamics and geometric group theory with connections to geometry and topology, ring and module theory, automata theory and theoretical computer science. Each solution is detailed and entirely self-contained, in the sense that it only requires a standard undergraduate-level background in abstract algebra and general topology, together with results established in [CAG] and in previous exercises. It includes a wealth of gradually worked out examples and counterexamples presented here for the first time in textbook form. Additional comments provide some historical and bibliographical information, including an account of related recent developments and suggestions for further reading. The eight-chapter division from [CAG] is maintained. Each chapter begins with a summary of the main definitions and results contained in the corresponding chapter of [CAG]. The book is suitable either for classroom or individual use. Foreword by Rostislav I. Grigorchuk

Author : W.C. Holland
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 53,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461334439

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Ordered Groups and Infinite Permutation Groups by W.C. Holland Pdf

The subjects of ordered groups and of infinite permutation groups have long en joyed a symbiotic relationship. Although the two subjects come from very different sources, they have in certain ways come together, and each has derived considerable benefit from the other. My own personal contact with this interaction began in 1961. I had done Ph. D. work on sequence convergence in totally ordered groups under the direction of Paul Conrad. In the process, I had encountered "pseudo-convergent" sequences in an ordered group G, which are like Cauchy sequences, except that the differences be tween terms of large index approach not 0 but a convex subgroup G of G. If G is normal, then such sequences are conveniently described as Cauchy sequences in the quotient ordered group GIG. If G is not normal, of course GIG has no group structure, though it is still a totally ordered set. The best that can be said is that the elements of G permute GIG in an order-preserving fashion. In independent investigations around that time, both P. Conrad and P. Cohn had showed that a group admits a total right ordering if and only if the group is a group of automor phisms of a totally ordered set. (In a right ordered group, the order is required to be preserved by all right translations, unlike a (two-sided) ordered group, where both right and left translations must preserve the order.

Author : Tullio Ceccherini-Silberstein,Michel Coornaert
Publisher : Springer Nature
Page : 562 pages
File Size : 46,7 Mb
Release : 2024-02-16
Category : Mathematics
ISBN : 9783031433283

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Cellular Automata and Groups by Tullio Ceccherini-Silberstein,Michel Coornaert Pdf

This unique book provides a self-contained exposition of the theory of cellular automata on groups and explores its deep connections with recent developments in geometric and combinatorial group theory, amenability, symbolic dynamics, the algebraic theory of group rings, and other branches of mathematics and theoretical computer science. The topics treated include the Garden of Eden theorem for amenable groups, the Gromov–Weiss surjunctivity theorem, and the solution of the Kaplansky conjecture on the stable finiteness of group rings for sofic groups. Entirely self-contained and now in its second edition, the volume includes 10 appendices and more than 600 exercises, the solutions of which are presented in the companion book Exercises in Cellular Automata and Groups (2023) by the same authors. It will appeal to a large audience, including specialists and newcomers to the field.

Author : A.C. Kim,D.L. Johnson
Publisher : Walter de Gruyter
Page : 357 pages
File Size : 55,6 Mb
Release : 2011-06-15
Category : Mathematics
ISBN : 9783110908978

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Groups - Korea 94 by A.C. Kim,D.L. Johnson Pdf

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Author : Jorge Martínez,W.C. Holland
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401117234

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Ordered Algebraic Structures by Jorge Martínez,W.C. Holland Pdf

This volume contains a selection of papers presented at the 1991 Conrad Conference, held in Gainesville, Florida, USA, in December, 1991. Together, these give an overview of some recent advances in the area of ordered algebraic structures. The first part of the book is devoted to ordered permutation groups and universal, as well as model-theoretic, aspects. The second part deals with material variously connected to general topology and functional analysis. Collectively, the contents of the book demonstrate the wide applicability of order-theoretic methods, and how ordered algebraic structures have connections with many research disciplines. For researchers and graduate students whose work involves ordered algebraic structures.

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 543 pages
File Size : 54,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401512336

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fme subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Author : W. Charles Holland
Publisher : CRC Press
Page : 216 pages
File Size : 44,6 Mb
Release : 2001-04-01
Category : Mathematics
ISBN : 9781482283150

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Ordered Algebraic Structures by W. Charles Holland Pdf

This book is an outcome of the conference on ordered algebraic structures held at Nanjing. It covers a range of topics: lattice theory, ordered semi groups, partially ordered groups, totally ordered groups, lattice-ordered groups, and ordered fields.

Author : M. Hazewinkel
Publisher : Springer
Page : 932 pages
File Size : 52,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781489937919

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Encyclopaedia of Mathematics by M. Hazewinkel Pdf

Author : Garrett Birkhoff
Publisher : American Mathematical Soc.
Page : 434 pages
File Size : 42,8 Mb
Release : 1940-12-31
Category : Mathematics
ISBN : 9780821810255

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Lattice Theory by Garrett Birkhoff Pdf

Since its original publication in 1940, this book has been revised and modernized several times, most notably in 1948 (second edition) and in 1967 (third edition). The material is organized into four main parts: general notions and concepts of lattice theory (Chapters I-V), universal algebra (Chapters VI-VII), applications of lattice theory to various areas of mathematics (Chapters VIII-XII), and mathematical structures that can be developed using lattices (Chapters XIII-XVII). At the end of the book there is a list of 166 unsolved problems in lattice theory, many of which still remain open. It is excellent reading, and ... the best place to start when one wishes to explore some portion of lattice theory or to appreciate the general flavor of the field. --Bulletin of the AMS