Infinite Group Theory
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Infinite Group Theory From The Past To The Future
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Author : Fine Benjamin
language : en
Publisher: World Scientific
Release Date : 2017-12-26
Infinite Group Theory From The Past To The Future written by Fine Benjamin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-26 with Mathematics categories.
The development of algebraic geometry over groups, geometric group theory and group-based cryptography, has led to there being a tremendous recent interest in infinite group theory. This volume presents a good collection of papers detailing areas of current interest. Contents: Groups with the Weak Minimal Condition on Non-Permutable Subgroups (Laxmi K Chatuat and Martyn R Dixon)A Survey: Shamir Threshold Scheme and Its Enhancements (Chi Sing Chum, Benjamin Fine, and Xiaowen Zhang)The Zappa-Szep Product of Left-Orderable Groups (Fabienne Chouraqui)Totally Disconnected Groups From Baumslag-Solitar Groups (Murray Elder and George Willis)Elementary and Universal Theories of Nonabelian Commutative Transitive and CSA Groups (B Fine, A M Gaglione, and D Spellman)Commutative Transitivity and the CSA Property (Benjamin Fine, Anthony Gaglione, Gerhard Rosenberger, and Dennis Spellman)The Universal Theory of Free Burnside Groups of Large Prime Exponent (Anthony M Gaglione, Seymour Lipschutz, and Dennis Spellman)Primitive Curve Lengths on Pairs of Pants (Jane Gilman)Drawing Inferences Under Maximum Entropy From Relational Probabilistic Knowledge Using Group Theory (Gabriele Kern-Isberner, Marco Wilhelm, and Christoph Beierle)On Some Infinite-Dimensional Linear Groups and the Structure of Related Modules (L A Kurdachenko and I Ya Subbotin)On New Analogs of Some Classical Group Theoretical Results in Lie Rings (L A Kurdachenko, A A Pypka and I Ya Subbotin)Log-Space Complexity of the Conjugacy Problem in Wreath Products (Alexei Myasnikov, Svetla Vassileva, and Armin Weiss)Group Presentations, Cayley Graphs and Markov Processes (Peter Olszewski) Readership: Graduate students and researchers in group theory. Keywords: Infinite Group Theory;Combinatorial Group Theory;Geometric Group TheoryReview: Key Features: This book is centered on infinite group theory from a combinatorial and geometric point of view. It also contains material on non-commutative algebraic group-based cryptography
Infinite Groups
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Author : Martyn R. Dixon
language : en
Publisher: CRC Press
Release Date : 2022-12-30
Infinite Groups written by Martyn R. Dixon and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-30 with Mathematics categories.
In recent times, group theory has found wider applications in various fields of algebra and mathematics in general. But in order to apply this or that result, you need to know about it, and such results are often diffuse and difficult to locate, necessitating that readers construct an extended search through multiple monographs, articles, and papers. Such readers must wade through the morass of concepts and auxiliary statements that are needed to understand the desired results, while it is initially unclear which of them are really needed and which ones can be dispensed with. A further difficulty that one may encounter might be concerned with the form or language in which a given result is presented. For example, if someone knows the basics of group theory, but does not know the theory of representations, and a group theoretical result is formulated in the language of representation theory, then that person is faced with the problem of translating this result into the language with which they are familiar, etc. Infinite Groups: A Roadmap to Some Classical Areas seeks to overcome this challenge. The book covers a broad swath of the theory of infinite groups, without giving proofs, but with all the concepts and auxiliary results necessary for understanding such results. In other words, this book is an extended directory, or a guide, to some of the more established areas of infinite groups. Features An excellent resource for a subject formerly lacking an accessible and in-depth reference Suitable for graduate students, PhD students, and researchers working in group theory Introduces the reader to the most important methods, ideas, approaches, and constructions in infinite group theory.
Aspects Of Infinite Groups
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Author : Benjamin Fine
language : en
Publisher: World Scientific
Release Date : 2008
Aspects Of Infinite Groups written by Benjamin Fine and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This book is a festschrift in honor of Professor Anthony Gaglione''s sixtieth birthday. This volume presents an excellent mix of research and expository articles on various aspects of infinite group theory. The papers give a broad overview of present research in infinite group theory in general, and combinatorial group theory and non-Abelian group-based cryptography in particular. They also pinpoint the interactions between combinatorial group theory and mathematical logic, especially model theory.
Topics In Infinite Group Theory
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Author : Benjamin Fine
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-08-23
Topics In Infinite Group Theory written by Benjamin Fine and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-23 with Mathematics categories.
This book gives an advanced overview of several topics in infinite group theory. It can also be considered as a rigorous introduction to combinatorial and geometric group theory. The philosophy of the book is to describe the interaction between these two important parts of infinite group theory. In this line of thought, several theorems are proved multiple times with different methods either purely combinatorial or purely geometric while others are shown by a combination of arguments from both perspectives. The first part of the book deals with Nielsen methods and introduces the reader to results and examples that are helpful to understand the following parts. The second part focuses on covering spaces and fundamental groups, including covering space proofs of group theoretic results. The third part deals with the theory of hyperbolic groups. The subjects are illustrated and described by prominent examples and an outlook on solved and unsolved problems.
Infinite Group Theory
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Author : Paul Baginski
language : en
Publisher:
Release Date : 2018
Infinite Group Theory written by Paul Baginski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Electronic books categories.
"The development of algebraic geometry over groups, geometric group theory and group-based cryptography, has led to there being a tremendous recent interest in infinite group theory. This volume presents a good collection of papers detailing areas of current interest."--
The Theory Of Infinite Soluble Groups
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Author : John C. Lennox
language : en
Publisher: Clarendon Press
Release Date : 2004-08-19
The Theory Of Infinite Soluble Groups written by John C. Lennox and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-19 with Mathematics categories.
The central concept in this monograph is that of a soluble group - a group which is built up from abelian groups by repeatedly forming group extensions. It covers all the major areas, including finitely generated soluble groups, soluble groups of finite rank, modules over group rings, algorithmic problems, applications of cohomology, and finitely presented groups, whilst remaining fairly strictly within the boundaries of soluble group theory. An up-to-date survey of the area aimed at research students and academic algebraists and group theorists, it is a compendium of information that will be especially useful as a reference work for researchers in the field.
Infinite Linear Groups
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Author : Bertram Wehrfritz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Infinite Linear Groups written by Bertram Wehrfritz 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.
By a linear group we mean essentially a group of invertible matrices with entries in some commutative field. A phenomenon of the last twenty years or so has been the increasing use of properties of infinite linear groups in the theory of (abstract) groups, although the story of infinite linear groups as such goes back to the early years of this century with the work of Burnside and Schur particularly. Infinite linear groups arise in group theory in a number of contexts. One of the most common is via the automorphism groups of certain types of abelian groups, such as free abelian groups of finite rank, torsion-free abelian groups of finite rank and divisible abelian p-groups of finite rank. Following pioneering work of Mal'cev many authors have studied soluble groups satisfying various rank restrictions and their automor phism groups in this way, and properties of infinite linear groups now play the central role in the theory of these groups. It has recently been realized that the automorphism groups of certain finitely generated soluble (in particular finitely generated metabelian) groups contain significant factors isomorphic to groups of automorphisms of finitely generated modules over certain commutative Noetherian rings. The results of our Chapter 13, which studies such groups of automorphisms, can be used to give much information here.
Infinite Group Rings
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Author : Donald S. Passman
language : en
Publisher:
Release Date : 1971
Infinite Group Rings written by Donald S. Passman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.
The algebraic study of group rings was initiated in 1949 by I. Kaplansky. The subject has been pursued by a small but growing number of researchers, and has reached a point in its development where a coherent account of the basic results is needed. That is the goal of this text. The topics covered are selective, with material balanced between ring theory and group theory, and a basic one year course in algebra should provide sufficient background for readers.
Infinite Groups Geometric Combinatorial And Dynamical Aspects
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Author : Laurent Bartholdi
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-28
Infinite Groups Geometric Combinatorial And Dynamical Aspects written by Laurent Bartholdi 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 2006-03-28 with Mathematics categories.
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.
Geometric Group Theory Asymptotic Invariants Of Infinite Groups
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Author : Graham A. Niblo
language : en
Publisher:
Release Date : 1993
Geometric Group Theory Asymptotic Invariants Of Infinite Groups written by Graham A. Niblo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Geometric group theory categories.