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The Restricted Burnside Problem
The first edition of this book provided an account of the restricted Burnside problem making extensive use of Lie ring techniques to provide a uniform treatment of the field. It also included Kostrikin's theorem for groups of prime exponent. The second edition, as well as providing general updating, contains a new chapter on E.I. Zelmanov's highly acclaimed and recent solution to the Restricted Burnside Problem for arbitrary prime-power exponent. This material is currently only available in papers in Russian journals. This proof ofZelmanov's theorem given in the new edition is self contained, and (unlike Zelmanov's original proof) does not rely on the theory of Jordan algebras.
The Restricted Burnside Problem
In 1902, William Burnside wrote: "A still undecided point in the theory of discontinuous groups is whether the order of a group many not be finite while the order of every operation it contains is finite." Since then, the Burnside problem, in different guises, has inspired a considerable amount of research. One variant of the Burnside problem, the restricted Burnside problem, asks whether (for a given r and n) there is a bound on the orders of finite r-generator groups of exponent n. This book provides the first comprehensive account of the many recent results in this area. By making extensive use of Lie ring techniques it allows a uniform treatment of the field and includes Kostrikin's theorem for groups of prime exponent as well as detailed information on groups of small (3,4,5,6,7,8,9) exponent. The treatment is intended to be self-contained and as such will be an invaluable introduction for postgraduate students and research workers. Included are extensive details of the use of computer algebra to verify computations.
Groups St Andrews 2001 in Oxford: Volume 2
This second volume of the two-volume book contains selected papers from the conference 'Groups St Andrews 2001 in Oxford'. The articles are contributed by a number of leading researchers and cover a wide spectrum of modern group theory. There are articles based on lecture courses given by five main speakers together with refereed survey and research articles. The 'Groups St Andrews' proceedings volumes are a snapshot of the state of the art in group theory and they often play an important role in future developments in the subject.
An Introduction to Local Spectral Theory
Modern local spectral theory is built on the classical spectral theorem, a fundamental result in single-operator theory and Hilbert spaces. This book provides an in-depth introduction to the natural expansion of this fascinating topic of Banach space operator theory, whose pioneers include Dunford, Bishop, Foias, and others. Assuming only modest prerequisites of its readership, it gives complete coverage of the field, including the fundamental recent work by Albrecht and Eschmeier which provides the full duality theory for Banach space operators. It is highlighted by many characterizations of decomposable operators, and of other related, important classes of operators, as well as an in-depth...
Operator Algebras and Their Modules
This invaluable reference is the first to present the general theory of algebras of operators on a Hilbert space, and the modules over such algebras. The new theory of operator spaces is presented early on and the text assembles the basic concepts, theory and methodologies needed to equip a beginning researcher in this area. A major trend in modern mathematics, inspired largely by physics, is toward noncommutative' or quantized' phenomena. In functional analysis, this has appeared notably under the name of operator spaces', which is a variant of Banach spaces which is particularly appropriate for solving problems concerning spaces or algebras of operators on Hilbert space arising in 'noncomm...
Harmonic Morphisms Between Riemannian Manifolds
This is an account in book form of the theory of harmonic morphisms between Riemannian manifolds.
Computational and Geometric Aspects of Modern Algebra
A collection of papers from leading researchers in algebra and geometric group theory.
The Mysteries of the Real Prime
Highly topical and original monograph, introducing the author's work on the Riemann zeta function and its adelic interpretation of interest to a wide range of mathematicians and physicists.
Interpolation, Identification, and Sampling
With this text, Jonathan Partington explores the application of mathematical analysis to problems of interpolation and engineering, including systems identification, and signal processing and sampling.
Super-real Fields
Super-fields are a class of totally ordered fields that are larger than the real line. They arise from quotients of the algebra of continuous functions on a compact space by a prime ideal, and generalize the well-known class of ultrapowers, and indeed the continuous ultrapowers. These fields are an important topic in their own right and have many surprising applications in analysis and logic. The authors introduce these exciting new fields to mathematicians, analysts, and logicians, including a natural generalization of the real line R, and resolve a number of open problems. After an exposition of the general theory of ordered fields and a careful proof of some classic theorems, including Kapansky's embedding, they establish important new results in Banach algebra theory, non-standard analysis, and model theory.
