Language: English
Published by World Scientific Publishing Comp, 2002
ISBN 10: 9810247834 ISBN 13: 9789810247836
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Language: English
Published by World Scientific Publishing Co Pte Ltd, SG, 2026
ISBN 10: 9819827442 ISBN 13: 9789819827442
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Hardback. Condition: New. This book is devoted to examining a range of results and related research stemming from the following classical theorem: If the center of a group has finite index, then the derived subgroup of the group is finite.This theorem, long regarded as a cornerstone of group theory, has played a significant role in the development of infinite group theory. The body of work in which it appears is extensive. It has had a profound influence on the field, serving as a catalyst for numerous results and inspiring new approaches to the study of infinite groups. These developments have helped shape the branch of infinite group theory now commonly referred to as the "classical" theory.
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Language: English
Published by Springer International Publishing, Springer Nature Switzerland, 2025
ISBN 10: 3031581504 ISBN 13: 9783031581502
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Language: English
Published by John Wiley and Sons Inc, US, 2017
ISBN 10: 1119080274 ISBN 13: 9781119080275
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Hardback. Condition: New. 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.
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Taschenbuch. Condition: Neu. General Theory of Leibniz Algebras | Leonid Kurdachenko (u. a.) | Taschenbuch | Synthesis Lectures on Mathematics & Statistics | x | Englisch | 2025 | Springer | EAN 9783031581502 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.
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Language: English
Published by Springer International Publishing, Springer Nature Switzerland, 2024
ISBN 10: 3031581474 ISBN 13: 9783031581472
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Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book discusses many interesting results have been obtained in Leibniz algebras over the past two decades. The authors not only summarize recent results and methods successfully used in Leibniz algebras, but also show new prospective horizons. Any mathematical theories have a number of natural problems that arise in the process of its development, and these problems quite often have analogues in other areas such as differential geometry, homological algebra, classical algebraic topology, noncommutative geometry, etc. With this in mind the authors describe the general structure of Leibniz algebras that have already been discovered. This approach allows readers tosee which parts of the theory should be developed further and also shows the significant differences of Leibniz algebras from Lie algebras. Recent results that constitute the naturally evolving general theory of the subject are then explored.
Language: English
Published by World Scientific Publishing Company, 2026
ISBN 10: 9819827442 ISBN 13: 9789819827442
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Language: English
Published by Taylor & Francis Ltd, 2020
ISBN 10: 1138542806 ISBN 13: 9781138542808
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Condition: Hervorragend. Zustand: Hervorragend | Seiten: 314 | Sprache: Englisch | Produktart: Bücher | Linear Groups: The Accent on Infinite Dimensionality explores some of the main results and ideas in the study of infinite-dimensional linear groups. The theory of finite dimensional linear groups is one of the best developed algebraic theories. The array of articles devoted to this topic is enormous, and there are many monographs concerned with matrix groups, ranging from old, classical texts to ones published more recently. However, in the case when the dimension is infinite (and such cases arise quite often), the reality is quite different. The situation with the study of infinite dimensional linear groups is like the situation that has developed in the theory of groups, in the transition from the study of finite groups to the study of infinite groups which appeared about one hundred years ago. It is well known that this transition was extremely efficient and led to the development of a rich and central branch of algebra: Infinite group theory.The hope is that this book can be part of a similar transition in the field of linear groups.FeaturesThis is the first book dedicated to infinite-dimensional linear groupsThis is written for experts and graduate students specializing in algebra and parallel disciplinesThis book discusses a very new theory and accumulates many important and useful results.
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Language: English
Published by John Wiley & Sons Inc, 2017
ISBN 10: 1119080274 ISBN 13: 9781119080275
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