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The Theory Of Nilpotent Groups
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Book Synopsis The Theory of Nilpotent Groups by : Anthony E. Clement
Download or read book The Theory of Nilpotent Groups written by Anthony E. Clement and published by Birkhäuser. This book was released on 2017-11-18 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents both classical and recent results in the theory of nilpotent groups and provides a self-contained, comprehensive reference on the topic. While the theorems and proofs included can be found throughout the existing literature, this is the first book to collect them in a single volume. Details omitted from the original sources, along with additional computations and explanations, have been added to foster a stronger understanding of the theory of nilpotent groups and the techniques commonly used to study them. Topics discussed include collection processes, normal forms and embeddings, isolators, extraction of roots, P-localization, dimension subgroups and Lie algebras, decision problems, and nilpotent groups of automorphisms. Requiring only a strong undergraduate or beginning graduate background in algebra, graduate students and researchers in mathematics will find The Theory of Nilpotent Groups to be a valuable resource.
Book Synopsis Quantization on Nilpotent Lie Groups by : Veronique Fischer
Download or read book Quantization on Nilpotent Lie Groups written by Veronique Fischer and published by Birkhäuser. This book was released on 2016-03-08 with total page 557 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a consistent development of the Kohn-Nirenberg type global quantization theory in the setting of graded nilpotent Lie groups in terms of their representations. It contains a detailed exposition of related background topics on homogeneous Lie groups, nilpotent Lie groups, and the analysis of Rockland operators on graded Lie groups together with their associated Sobolev spaces. For the specific example of the Heisenberg group the theory is illustrated in detail. In addition, the book features a brief account of the corresponding quantization theory in the setting of compact Lie groups. The monograph is the winner of the 2014 Ferran Sunyer i Balaguer Prize.
Book Synopsis Nilpotent Groups and their Automorphisms by : Evgenii I. Khukhro
Download or read book Nilpotent Groups and their Automorphisms written by Evgenii I. Khukhro and published by Walter de Gruyter. This book was released on 2011-04-20 with total page 269 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 Localization of Nilpotent Groups and Spaces by : Peter Hilton
Download or read book Localization of Nilpotent Groups and Spaces written by Peter Hilton and published by Elsevier. This book was released on 2016-06-03 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: North-Holland Mathematics Studies, 15: Localization of Nilpotent Groups and Spaces focuses on the application of localization methods to nilpotent groups and spaces. The book first discusses the localization of nilpotent groups, including localization theory of nilpotent groups, properties of localization in N, further properties of localization, actions of a nilpotent group on an abelian group, and generalized Serre classes of groups. The book then examines homotopy types, as well as mixing of homotopy types, localizing H-spaces, main (pullback) theorem, quasifinite nilpotent spaces, localization of nilpotent complexes, and nilpotent spaces. The manuscript takes a look at the applications of localization theory, including genus and H-spaces, finite H-spaces, and non-cancellation phenomena. The publication is a vital source of data for mathematicians and researchers interested in the localization of nilpotent groups and spaces.
Book Synopsis Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras by : Martin W. Liebeck
Download or read book Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras written by Martin W. Liebeck and published by American Mathematical Soc.. This book was released on 2012-01-25 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concerns the theory of unipotent elements in simple algebraic groups over algebraically closed or finite fields, and nilpotent elements in the corresponding simple Lie algebras. These topics have been an important area of study for decades, with applications to representation theory, character theory, the subgroup structure of algebraic groups and finite groups, and the classification of the finite simple groups. The main focus is on obtaining full information on class representatives and centralizers of unipotent and nilpotent elements. Although there is a substantial literature on this topic, this book is the first single source where such information is presented completely in all characteristics. In addition, many of the results are new--for example, those concerning centralizers of nilpotent elements in small characteristics. Indeed, the whole approach, while using some ideas from the literature, is novel, and yields many new general and specific facts concerning the structure and embeddings of centralizers.
Book Synopsis Problems in Group Theory by : John D. Dixon
Download or read book Problems in Group Theory written by John D. Dixon and published by Courier Corporation. This book was released on 2007-01-01 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: 265 challenging problems in all phases of group theory, gathered for the most part from papers published since 1950, although some classics are included.
Book Synopsis Finite Group Theory by : I. Martin Isaacs
Download or read book Finite Group Theory written by I. Martin Isaacs and published by American Mathematical Society. This book was released on 2023-01-24 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text begins with a review of group actions and Sylow theory. It includes semidirect products, the Schur–Zassenhaus theorem, the theory of commutators, coprime actions on groups, transfer theory, Frobenius groups, primitive and multiply transitive permutation groups, the simplicity of the PSL groups, the generalized Fitting subgroup and also Thompson's J-subgroup and his normal $p$-complement theorem. Topics that seldom (or never) appear in books are also covered. These include subnormality theory, a group-theoretic proof of Burnside's theorem about groups with order divisible by just two primes, the Wielandt automorphism tower theorem, Yoshida's transfer theorem, the “principal ideal theorem” of transfer theory and many smaller results that are not very well known. Proofs often contain original ideas, and they are given in complete detail. In many cases they are simpler than can be found elsewhere. The book is largely based on the author's lectures, and consequently, the style is friendly and somewhat informal. Finally, the book includes a large collection of problems at disparate levels of difficulty. These should enable students to practice group theory and not just read about it. Martin Isaacs is professor of mathematics at the University of Wisconsin, Madison. Over the years, he has received many teaching awards and is well known for his inspiring teaching and lecturing. He received the University of Wisconsin Distinguished Teaching Award in 1985, the Benjamin Smith Reynolds Teaching Award in 1989, and the Wisconsin Section MAA Teaching Award in 1993, to name only a few. He was also honored by being the selected MAA Pólya Lecturer in 2003–2005.
Book Synopsis A Course in the Theory of Groups by : Derek J.S. Robinson
Download or read book A Course in the Theory of Groups written by Derek J.S. Robinson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: " A group is defined by means of the laws of combinations of its symbols," according to a celebrated dictum of Cayley. And this is probably still as good a one-line explanation as any. The concept of a group is surely one of the central ideas of mathematics. Certainly there are a few branches of that science in which groups are not employed implicitly or explicitly. Nor is the use of groups confined to pure mathematics. Quantum theory, molecular and atomic structure, and crystallography are just a few of the areas of science in which the idea of a group as a measure of symmetry has played an important part. The theory of groups is the oldest branch of modern algebra. Its origins are to be found in the work of Joseph Louis Lagrange (1736-1813), Paulo Ruffini (1765-1822), and Evariste Galois (1811-1832) on the theory of algebraic equations. Their groups consisted of permutations of the variables or of the roots of polynomials, and indeed for much of the nineteenth century all groups were finite permutation groups. Nevertheless many of the fundamental ideas of group theory were introduced by these early workers and their successors, Augustin Louis Cauchy (1789-1857), Ludwig Sylow (1832-1918), Camille Jordan (1838-1922) among others. The concept of an abstract group is clearly recognizable in the work of Arthur Cayley (1821-1895) but it did not really win widespread acceptance until Walther von Dyck (1856-1934) introduced presentations of groups.
Book Synopsis Theory of Nilpotent Groups by : Richard Tolimieri
Download or read book Theory of Nilpotent Groups written by Richard Tolimieri and published by . This book was released on 1970 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nilpotent Groups by : R.B. Jr. Warfield
Download or read book Nilpotent Groups written by R.B. Jr. Warfield 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:
Book Synopsis Algebraic Theory of Locally Nilpotent Derivations by : Gene Freudenburg
Download or read book Algebraic Theory of Locally Nilpotent Derivations written by Gene Freudenburg and published by Springer Science & Business Media. This book was released on 2007-07-18 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the theory and application of locally nilpotent derivations. It provides a unified treatment of the subject, beginning with sixteen First Principles on which the entire theory is based. These are used to establish classical results, such as Rentschler’s Theorem for the plane, right up to the most recent results, such as Makar-Limanov’s Theorem for locally nilpotent derivations of polynomial rings. The book also includes a wealth of pexamples and open problems.
Book Synopsis Characters of Solvable Groups by : I. Martin Isaacs
Download or read book Characters of Solvable Groups written by I. Martin Isaacs and published by American Mathematical Soc.. This book was released on 2018-05-23 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, which can be considered as a sequel of the author's famous book Character Theory of Finite Groups, concerns the character theory of finite solvable groups and other groups that have an abundance of normal subgroups. It is subdivided into three parts: -theory, character correspondences, and M-groups. The -theory section contains an exposition of D. Gajendragadkar's -special characters, and it includes various extensions, generalizations, and applications of his work. The character correspondences section proves the McKay character counting conjecture and the Alperin weight conjecture for solvable groups, and it constructs a canonical McKay bijection for odd-order groups. In addition to a review of some basic material on M-groups, the third section contains an exposition of the use of symplectic modules for studying M-groups. In particular, an accessible presentation of E. C. Dade's deep results on monomial characters of odd prime-power degree is included. Very little of this material has previously appeared in book form, and much of it is based on the author's research. By reading a clean and accessible presentation written by the leading expert in the field, researchers and graduate students will be inspired to learn and work in this area that has fascinated the author for decades.
Book Synopsis Representations of Nilpotent Lie Groups and Their Applications by : Lawrence J. Corwin
Download or read book Representations of Nilpotent Lie Groups and Their Applications written by Lawrence J. Corwin and published by . This book was released on 1990 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Approximate Groups by : Matthew C. H. Tointon
Download or read book Introduction to Approximate Groups written by Matthew C. H. Tointon and published by Cambridge University Press. This book was released on 2019-11-14 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Approximate groups have shot to prominence in recent years, driven both by rapid progress in the field itself and by a varied and expanding range of applications. This text collects, for the first time in book form, the main concepts and techniques into a single, self-contained introduction. The author presents a number of recent developments in the field, including an exposition of his recent result classifying nilpotent approximate groups. The book also features a considerable amount of previously unpublished material, as well as numerous exercises and motivating examples. It closes with a substantial chapter on applications, including an exposition of Breuillard, Green and Tao's celebrated approximate-group proof of Gromov's theorem on groups of polynomial growth. Written by an author who is at the forefront of both researching and teaching this topic, this text will be useful to advanced students and to researchers working in approximate groups and related areas.
Book Synopsis Nilpotence and Periodicity in Stable Homotopy Theory by : Douglas C. Ravenel
Download or read book Nilpotence and Periodicity in Stable Homotopy Theory written by Douglas C. Ravenel and published by Princeton University Press. This book was released on 1992-11-08 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins, and Smith in 1985. During the last ten years a number of significant advances have been made in homotopy theory, and this book fills a real need for an up-to-date text on that topic. Ravenel's first few chapters are written with a general mathematical audience in mind. They survey both the ideas that lead up to the theorems and their applications to homotopy theory. The book begins with some elementary concepts of homotopy theory that are needed to state the problem. This includes such notions as homotopy, homotopy equivalence, CW-complex, and suspension. Next the machinery of complex cobordism, Morava K-theory, and formal group laws in characteristic p are introduced. The latter portion of the book provides specialists with a coherent and rigorous account of the proofs. It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.
Download or read book Groups written by Antonio Machì and published by Springer Science & Business Media. This book was released on 2012-04-05 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Groups are a means of classification, via the group action on a set, but also the object of a classification. How many groups of a given type are there, and how can they be described? Hölder’s program for attacking this problem in the case of finite groups is a sort of leitmotiv throughout the text. Infinite groups are also considered, with particular attention to logical and decision problems. Abelian, nilpotent and solvable groups are studied both in the finite and infinite case. Permutation groups and are treated in detail; their relationship with Galois theory is often taken into account. The last two chapters deal with the representation theory of finite group and the cohomology theory of groups; the latter with special emphasis on the extension problem. The sections are followed by exercises; hints to the solution are given, and for most of them a complete solution is provided.
Book Synopsis Finite Groups by : Bertram A. F. Wehrfritz
Download or read book Finite Groups written by Bertram A. F. Wehrfritz and published by World Scientific. This book was released on 1999 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of groups, especially of finite groups, is one of the most delightful areas of mathematics. Its proofs often have elegance and crystalline beauty. This textbook is intended for the reader who has been exposed to about three years of serious mathematics. The notion of a group appears widely in mathematics and even further afield in physics and chemistry, and the fundamental idea should be known to all mathematicians. In this textbook a purely algebraic approach is taken and the choice of material is based upon the notion of conjugacy. The aim is not only to cover basic material, but also to present group theory as a living, vibrant and growing discipline, by including references and discussion of some work up to the present day.