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The Lattice Of Normal Subgroups Of An Infinite Group
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Book Synopsis Subgroup Lattices of Groups by : Roland Schmidt
Download or read book Subgroup Lattices of Groups written by Roland Schmidt and published by Walter de Gruyter. This book was released on 2011-07-20 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany
Book Synopsis New Horizons in pro-p Groups by : Marcus du Sautoy
Download or read book New Horizons in pro-p Groups written by Marcus du Sautoy and published by Springer Science & Business Media. This book was released on 2000-05-25 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: A pro-p group is the inverse limit of some system of finite p-groups, that is, of groups of prime-power order where the prime - conventionally denoted p - is fixed. Thus from one point of view, to study a pro-p group is the same as studying an infinite family of finite groups; but a pro-p group is also a compact topological group, and the compactness works its usual magic to bring 'infinite' problems down to manageable proportions. The p-adic integers appeared about a century ago, but the systematic study of pro-p groups in general is a fairly recent development. Although much has been dis covered, many avenues remain to be explored; the purpose of this book is to present a coherent account of the considerable achievements of the last several years, and to point the way forward. Thus our aim is both to stimulate research and to provide the comprehensive background on which that research must be based. The chapters cover a wide range. In order to ensure the most authoritative account, we have arranged for each chapter to be written by a leading contributor (or contributors) to the topic in question. Pro-p groups appear in several different, though sometimes overlapping, contexts.
Book Synopsis Infinite Groups: Geometric, Combinatorial and Dynamical Aspects by : Laurent Bartholdi
Download or read book Infinite Groups: Geometric, Combinatorial and Dynamical Aspects written by Laurent Bartholdi and published by Springer Science & Business Media. This book was released on 2006-03-28 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Infinite Groups 1994 by : Francesco Giovanni
Download or read book Infinite Groups 1994 written by Francesco Giovanni and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-03-06 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis New Horizons in pro-p Groups by : Marcus du Sautoy
Download or read book New Horizons in pro-p Groups written by Marcus du Sautoy and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: A pro-p group is the inverse limit of some system of finite p-groups, that is, of groups of prime-power order where the prime - conventionally denoted p - is fixed. Thus from one point of view, to study a pro-p group is the same as studying an infinite family of finite groups; but a pro-p group is also a compact topological group, and the compactness works its usual magic to bring 'infinite' problems down to manageable proportions. The p-adic integers appeared about a century ago, but the systematic study of pro-p groups in general is a fairly recent development. Although much has been dis covered, many avenues remain to be explored; the purpose of this book is to present a coherent account of the considerable achievements of the last several years, and to point the way forward. Thus our aim is both to stimulate research and to provide the comprehensive background on which that research must be based. The chapters cover a wide range. In order to ensure the most authoritative account, we have arranged for each chapter to be written by a leading contributor (or contributors) to the topic in question. Pro-p groups appear in several different, though sometimes overlapping, contexts.
Download or read book Algebra written by Yuri Bahturin and published by Walter de Gruyter. This book was released on 2011-05-02 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Theory of Groups by : Hans J. Zassenhaus
Download or read book The Theory of Groups written by Hans J. Zassenhaus and published by Courier Corporation. This book was released on 2013-09-16 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Well-written graduate-level text acquaints reader with group-theoretic methods and demonstrates their usefulness in mathematics. Axioms, the calculus of complexes, homomorphic mapping, p-group theory, more. Many proofs shorter and more transparent than older ones.
Book Synopsis Linear Pro-p-Groups of Finite Width by : Gundel Klaas
Download or read book Linear Pro-p-Groups of Finite Width written by Gundel Klaas and published by Springer. This book was released on 2006-11-14 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: The normal subgroup structure of maximal pro-p-subgroups of rational points of algebraic groups over the p-adics and their characteristic p analogues are investigated. These groups have finite width, i.e. the indices of the sucessive terms of the lower central series are bounded since they become periodic. The richness of the lattice of normal subgroups is studied by the notion of obliquity. All just infinite maximal groups with Lie algebras up to dimension 14 and most Chevalley groups and classical groups in characteristic 0 and p are covered. The methods use computers in small cases and are purely theoretical for the infinite series using root systems or orders with involutions.
Book Synopsis Infinite Groups by : Martyn R. Dixon
Download or read book Infinite Groups written by Martyn R. Dixon and published by CRC Press. This book was released on 2022-12-30 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Integrable Systems and Algebraic Geometry: Volume 2 by : Ron Donagi
Download or read book Integrable Systems and Algebraic Geometry: Volume 2 written by Ron Donagi and published by Cambridge University Press. This book was released on 2020-04-02 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many of whom have been at the forefront of research into these topics for the last decades, have all been influenced by Previato's research, as her collaborators, students, or colleagues. The diverse articles in the book demonstrate the wide scope of Previato's work and the inclusion of several survey and introductory articles makes the text accessible to graduate students and non-experts, as well as researchers. The articles in this second volume discuss areas related to algebraic geometry, emphasizing the connections of this central subject to integrable systems, arithmetic geometry, Riemann surfaces, coding theory and lattice theory.
Book Synopsis Ranks of Groups by : Martyn R. Dixon
Download or read book Ranks of Groups written by Martyn R. Dixon and published by John Wiley & Sons. This book was released on 2017-06-15 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive guide to ranks and group theory Ranks of Groups features a logical, straightforward presentation, beginning with a succinct discussion of the standard ranks before moving on to specific aspects of ranks of groups. Topics covered include section ranks, groups of finite 0-rank, minimax rank, special rank, groups of finite section p-rank, groups having finite section p-rank for all primes p, groups of finite bounded section rank, groups whose abelian subgroups have finite rank, groups whose abelian subgroups have bounded finite rank, finitely generated groups having finite rank, residual properties of groups of finite rank, groups covered by normal subgroups of bounded finite rank, and theorems of Schur and Baer. This book presents fundamental concepts and notions related to the area of ranks in groups. Class-tested worldwide by highly qualified authors in the fields of abstract algebra and group theory, this book focuses on critical concepts with the most interesting, striking, and central results. In order to provide readers with the most useful techniques related to the various different ranks in a group, the authors have carefully examined hundreds of current research articles on group theory authored by researchers around the world, providing an up-to-date, comprehensive treatment of the subject. • All material has been thoroughly vetted and class-tested by well-known researchers who have worked in the area of rank conditions in groups • Topical coverage reflects the most modern, up-to-date research on ranks of groups • Features a unified point-of-view on the most important results in ranks obtained using various methods so as to illustrate the role those ranks play within group theory • Focuses on the tools and methods concerning ranks necessary to achieve significant progress in the study and clarification of the structure of groups Ranks of Groups: The Tools, Characteristics, and Restrictions is an excellent textbook for graduate courses in mathematics, featuring numerous exercises, whose solutions are provided. This book will be an indispensable resource for mathematicians and researchers specializing in group theory and abstract algebra. MARTYN R. DIXON, PhD, is Professor in the Department of Mathematics at the University of Alabama. LEONID A. KURDACHENKO, PhD, DrS, is Distinguished Professor and Chair of the Department of Algebra at the University of Dnepropetrovsk, Ukraine. IGOR YA SUBBOTIN, PhD, is Professor in the Department of Mathematics and Natural Sciences at National University in Los Angeles, California.
Book Synopsis Contemporary Problems In Mathematical Physics - Proceedings Of The Third International Workshop by : Jan Govaerts
Download or read book Contemporary Problems In Mathematical Physics - Proceedings Of The Third International Workshop written by Jan Govaerts and published by World Scientific. This book was released on 2004-12-08 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: The COPROMAPH Conference series has now evolved into a significant international arena where fundamental concepts in mathematical and theoretical physics and their physics applications can be conceived, developed and disseminated. Basic ideas for addressing a variety of contemporary problems in mathematical and theoretical physics are presented in a nonintimidating atmosphere. Experts provide the reader the fundamentals to predict new possibilities in physics and other fields.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences
Book Synopsis Groups St Andrews 2017 in Birmingham by : C. M. Campbell
Download or read book Groups St Andrews 2017 in Birmingham written by C. M. Campbell and published by Cambridge University Press. This book was released on 2019-04-11 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume arises from the 2017 edition of the long-running 'Groups St Andrews' conference series and consists of expository papers from leading researchers in all areas of group theory. It provides a snapshot of the state-of-the-art in the field, and it will be a valuable resource for researchers and graduate students.
Book Synopsis New Developments in Lie Theory and Geometry by : Carolyn Gordon
Download or read book New Developments in Lie Theory and Geometry written by Carolyn Gordon and published by American Mathematical Soc.. This book was released on 2009 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an outgrowth of the Sixth Workshop on Lie Theory and Geometry, held in the province of Cordoba, Argentina in November 2007. The representation theory and structure theory of Lie groups play a pervasive role throughout mathematics and physics. Lie groups are tightly intertwined with geometry and each stimulates developments in the other. The aim of this volume is to bring to a larger audience the mutually beneficial interaction between Lie theorists and geometers that animated the workshop. Two prominent themes of the representation theoretic articles are Gelfand pairs and the representation theory of real reductive Lie groups. Among the more geometric articles are an exposition of major recent developments on noncompact homogeneous Einstein manifolds and aspects of inverse spectral geometry presented in settings accessible to readers new to the area.
Download or read book Group Theory written by Otto H. Kegel and published by Springer. This book was released on 2006-11-15 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometry, Spectral Theory, Groups, and Dynamics by : Robert Brooks
Download or read book Geometry, Spectral Theory, Groups, and Dynamics written by Robert Brooks and published by American Mathematical Soc.. This book was released on 2005 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains articles based on talks given at the Robert Brooks Memorial Conference on Geometry and Spectral Theory and the Workshop on Groups, Geometry and Dynamics held at Technion - the Israel Institute of Technology (Haifa). Robert Brooks' (1952 - 2002) broad range of mathematical interests is represented in the volume, which is devoted to various aspects of global analysis, spectral theory, the theory of Riemann surfaces, Riemannian and discrete geometry, and numbertheory. A survey of Brooks' work has been written by his close colleague, Peter Buser. Also included in the volume are articles on analytic topics, such as Szego's theorem, and on geometric topics, such as isoperimetric inequalities and symmetries of manifolds. The book is suitable for graduate studentsand researchers interested in various aspects of geometry and global analysis.
Book Synopsis Structure of a Group and the Structure of its Lattice of Subgroups by : Michio Suzuki
Download or read book Structure of a Group and the Structure of its Lattice of Subgroups written by Michio Suzuki and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this monograph is the relation between the structure of a group and the structure of its lattice of subgroups. Since the first papers on this topic have appeared, notably those of BAER and ORE, a large body of literature has grown up around this theory, and it is our aim to give a picture of the present state of this theory. To obtain a systematic treatment of the subject quite a few unpublished results of the author had to be included. On the other hand, it is natural that we could not reproduce every detail and had to treat some parts some wh at sketchily. We have tried to make this report as self-contained as possible. Accordingly we have given some proofs in considerable detail, though of course it is in the nature of such areport that many proofs have to be omitted or can only be given in outline. Similarly references to the concepts and theorems used are almost exclusively references to standard works like BIRKHOFF [lJ and ZASSENHAUS [lJ. The author would like to express his sincere gratitude to Professors REINHOLD BAER and DONALD G. HIGMAN for their kindness in giving hirn many valuable suggestions. His thanks are also due to Dr. NOBORU ITo who, during stimulating conversations, contributed many useful ideas. Urbana, May, 1956. M. Suzuki. Contents.
