Symmetry

An Introduction to Group Theory and Its Applications

Author: R. McWeeny

Publisher: Elsevier

ISBN: 1483226247

Category: Mathematics

Page: 262

View: 5984

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Symmetry: An Introduction to Group Theory and its Application is an eight-chapter text that covers the fundamental bases, the development of the theoretical and experimental aspects of the group theory. Chapter 1 deals with the elementary concepts and definitions, while Chapter 2 provides the necessary theory of vector spaces. Chapters 3 and 4 are devoted to an opportunity of actually working with groups and representations until the ideas already introduced are fully assimilated. Chapter 5 looks into the more formal theory of irreducible representations, while Chapter 6 is concerned largely with quadratic forms, illustrated by applications to crystal properties and to molecular vibrations. Chapter 7 surveys the symmetry properties of functions, with special emphasis on the eigenvalue equation in quantum mechanics. Chapter 8 covers more advanced applications, including the detailed analysis of tensor properties and tensor operators. This book is of great value to mathematicians, and math teachers and students.

The Theory of Classes of Groups

Author: Guo Wenbin

Publisher: Springer Science & Business Media

ISBN: 9401140545

Category: Mathematics

Page: 258

View: 6277

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One of the characteristics of modern algebra is the development of new tools and concepts for exploring classes of algebraic systems, whereas the research on individual algebraic systems (e. g. , groups, rings, Lie algebras, etc. ) continues along traditional lines. The early work on classes of alge bras was concerned with showing that one class X of algebraic systems is actually contained in another class F. Modern research into the theory of classes was initiated in the 1930's by Birkhoff's work [1] on general varieties of algebras, and Neumann's work [1] on varieties of groups. A. I. Mal'cev made fundamental contributions to this modern development. ln his re ports [1, 3] of 1963 and 1966 to The Fourth All-Union Mathematics Con ference and to another international mathematics congress, striking the ories of classes of algebraic systems were presented. These were later included in his book [5]. International interest in the theory of formations of finite groups was aroused, and rapidly heated up, during this time, thanks to the work of Gaschiitz [8] in 1963, and the work of Carter and Hawkes [1] in 1967. The major topics considered were saturated formations, Fitting classes, and Schunck classes. A class of groups is called a formation if it is closed with respect to homomorphic images and subdirect products. A formation is called saturated provided that G E F whenever Gjip(G) E F.

Classes of Finite Groups

Author: Adolfo Ballester-Bollinches,Luis M. Ezquerro

Publisher: Springer Science & Business Media

ISBN: 1402047193

Category: Mathematics

Page: 381

View: 6116

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This book covers the latest achievements of the Theory of Classes of Finite Groups. It introduces some unpublished and fundamental advances in this Theory and provides a new insight into some classic facts in this area. By gathering the research of many authors scattered in hundreds of papers the book contributes to the understanding of the structure of finite groups by adapting and extending the successful techniques of the Theory of Finite Soluble Groups.

Group Theory and Its Application to Physical Problems

Author: Morton Hamermesh

Publisher: Courier Corporation

ISBN: 0486140393

Category: Science

Page: 544

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One of the best-written, most skillful expositions of group theory and its physical applications, directed primarily to advanced undergraduate and graduate students in physics, especially quantum physics. With problems.

The Theory of Groups and Quantum Mechanics

Author: Hermann Weyl

Publisher: Courier Corporation

ISBN: 9780486602691

Category: Mathematics

Page: 422

View: 6329

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This landmark among mathematics texts applies group theory to quantum mechanics, first covering unitary geometry, quantum theory, groups and their representations, then applications themselves — rotation, Lorentz, permutation groups, symmetric permutation groups, and the algebra of symmetric transformations.

A Course in the Theory of Groups

Author: Derek J.S. Robinson

Publisher: Springer Science & Business Media

ISBN: 1441985948

Category: Mathematics

Page: 502

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"An excellent up-to-date introduction to the theory of groups. It is general yet comprehensive, covering various branches of group theory. The 15 chapters contain the following main topics: free groups and presentations, free products, decompositions, Abelian groups, finite permutation groups, representations of groups, finite and infinite soluble groups, group extensions, generalizations of nilpotent and soluble groups, finiteness properties." —-ACTA SCIENTIARUM MATHEMATICARUM

Arboreal Group Theory

Proceedings of a Workshop Held September 13 - 16, 1988 [at the Mathematical Sciences Research Institute, Berkeley, CA]

Author: Roger C. Alperin

Publisher: Springer Science & Business Media

ISBN: 9780387975184

Category: Mathematics

Page: 368

View: 6217

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Contains the proceedings of the workshop on Arboreal Group Theory, which centered on the topic of the theory of groups acting on trees and the various applications to hyperbolic geometry. This book covers: structure of groups acting freely on trees, spaces of hyperbolic structures and their compactifications, and moduli for tree actions.

Mathematical Analysis and Its Applications

Proceedings of the International Conference on Mathematical Analysis and its Applications, Kuwait, 1985

Author: S. M. Mazhar,A. Hamoui,N. S. Faour

Publisher: Elsevier

ISBN: 1483148114

Category: Mathematics

Page: 442

View: 9224

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Mathematical Analysis and its Applications covers the proceedings of the International Conference on Mathematical Analysis and its Applications. The book presents studies that discuss several mathematical analysis methods and their respective applications. The text presents 38 papers that discuss topics, such as approximation of continuous functions by ultraspherical series and classes of bi-univalent functions. The representation of multipliers of eigen and joint function expansions of nonlocal spectral problems for first- and second-order differential operators is also discussed. The book will be of great interest to researchers and professionals whose work involves the use of mathematical analysis.

Group Theory in China

Author: Zhexian Wan

Publisher: Springer Science & Business Media

ISBN: 9780792339892

Category: Mathematics

Page: 261

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Hsio-Fu Tuan is a Chinese mathematician who has made important contributions to the theories of both finite groups and Lie groups. He has also had a great influence on the development of algebra, and particularly group theory in China. The present volume consists of a collection of essays on various aspects of group theory written by some of his former students and colleagues in honour of his 80th birthday. The papers contain the main general results, as well as recent ones, on certain topics within this discipline. The chief editor, Zhe-Xian Wan, is a leading algebraist in China.

The Theory and Applications of Harmonic Integrals

Author: W. V. D. Hodge

Publisher: CUP Archive

ISBN: 9780521358811

Category: Mathematics

Page: 284

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First published in 1941, this book, by one of the foremost geometers of his day, rapidly became a classic. In its original form the book constituted a section of Hodge's essay for which the Adam's prize of 1936 was awarded, but the author substantially revised and rewrote it. The book begins with an exposition of the geometry of manifolds and the properties of integrals on manifolds. The remainder of the book is then concerned with the application of the theory of harmonic integrals to other branches of mathematics, particularly to algebraic varieties and to continuous groups. Differential geometers and workers in allied subjects will welcome this reissue both for its lucid account of the subject and for its historical value. For this paperback edition, Professor Sir Michael Atiyah has written a foreword that sets Hodges work in its historical context and relates it briefly to developments.

Applications of the Theory of Groups in Mechanics and Physics

Author: Petre P. Teodorescu,Nicolae-A.P. Nicorovici

Publisher: Springer Science & Business Media

ISBN: 9781402020469

Category: Mathematics

Page: 446

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The notion of group is fundamental in our days, not only in mathematics, but also in classical mechanics, electromagnetism, theory of relativity, quantum mechanics, theory of elementary particles, etc. This notion has developed during a century and this development is connected with the names of great mathematicians as E. Galois, A. L. Cauchy, C. F. Gauss, W. R. Hamilton, C. Jordan, S. Lie, E. Cartan, H. Weyl, E. Wigner, and of many others. In mathematics, as in other sciences, the simple and fertile ideas make their way with difficulty and slowly; however, this long history would have been of a minor interest, had the notion of group remained connected only with rather restricted domains of mathematics, those in which it occurred at the beginning. But at present, groups have invaded almost all mathematical disciplines, mechanics, the largest part of physics, of chemistry, etc. We may say, without exaggeration, that this is the most important idea that occurred in mathematics since the invention of infinitesimal calculus; indeed, the notion of group expresses, in a precise and operational form, the vague and universal ideas of regularity and symmetry. The notion of group led to a profound understanding of the character of the laws which govern natural phenomena, permitting to formulate new laws, correcting certain inadequate formulations and providing unitary and non contradictory formulations for the investigated phenomena.

Formal Groups and Applications

Author: Michiel Hazewinkel

Publisher: American Mathematical Soc.

ISBN: 082185349X

Category: Mathematics

Page: 573

View: 8858

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This title provides a comprehensive treatment of the theory of formal groups and its numerous applications in several areas of mathematics. The seven chapters of the book present basics and main results of the theory, as well as very important applications in algebraic topology, number theory, and algebraic geometry.

Groups, Combinatorics and Geometry

DURHAM 2001

Author: A A Ivanov,M W Liebeck,J Saxl

Publisher: World Scientific

ISBN: 9814486426

Category: Mathematics

Page: 348

View: 1604

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Over the past 20 years, the theory of groups — in particular simple groups, finite and algebraic — has influenced a number of diverse areas of mathematics. Such areas include topics where groups have been traditionally applied, such as algebraic combinatorics, finite geometries, Galois theory and permutation groups, as well as several more recent developments. Among the latter are probabilistic and computational group theory, the theory of algebraic groups over number fields, and model theory, in each of which there has been a major recent impetus provided by simple group theory. In addition, there is still great interest in local analysis in finite groups, with substantial new input from methods of geometry and amalgams, and particular emphasis on the revision project for the classification of finite simple groups. This important book contains 20 survey articles covering many of the above developments. It should prove invaluable for those working in the theory of groups and its applications. Contents:Curtis–Phan–Tits Theory (C D Bennett et al.)Derangements in Simple and Primitive Groups (J Fulman & R Guralnick)Computing with Matrix Groups (W M Kantor & Á Seress)Bases of Primitive Permutation Groups (M W Liebeck & A Shalev)Modular Subgroup Arithmetic (T W Müller)Counting Nets in the Monster (S P Norton)Overgroups of Finite Quasiprimitive Permutation Groups (C E Praeger)Old Groups Can Learn New Tricks (L Pyber)Structure and Presentations of Lie-Type Groups (F G Timmesfeld)Computing in the Monster (R A Wilson)and other papers Readership: Graduate students, researchers and academics in algebra. Keywords:Simple Groups;Algebraic Combinatorics;Finite Geometry;Permutation Groups. Probabilistic Group

Structure Theory for Canonical Classes of Finite Groups

Author: Wenbin Guo

Publisher: Springer

ISBN: 3662457474

Category: Mathematics

Page: 359

View: 6727

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This book offers a systematic introduction to recent achievements and development in research on the structure of finite non-simple groups, the theory of classes of groups and their applications. In particular, the related systematic theories are considered and some new approaches and research methods are described – e.g., the F-hypercenter of groups, X-permutable subgroups, subgroup functors, generalized supplementary subgroups, quasi-F-group, and F-cohypercenter for Fitting classes. At the end of each chapter, we provide relevant supplementary information and introduce readers to selected open problems.

Encyclopaedia of Mathematics

Stochastic Approximation — Zygmund Class of Functions

Author: Michiel Hazewinkel

Publisher: Springer Science & Business Media

ISBN: 9781556080081

Category: Mathematics

Page: 536

View: 2130

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This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fme subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Applied Finite Group Actions

Author: Adalbert Kerber

Publisher: Springer Science & Business Media

ISBN: 3662111675

Category: Mathematics

Page: 454

View: 6990

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Written by one of the top experts in the fields of combinatorics and representation theory, this book distinguishes itself from the existing literature by its applications-oriented point of view. The second edition is extended, placing more emphasis on applications to the constructive theory of finite structures. Recent progress in this field, in particular in design and coding theory, is described.

Identities of Algebras and Their Representations

Author: I͡Uriĭ Pitirimovich Razmyslov

Publisher: American Mathematical Soc.

ISBN: 9780821846087

Category: Mathematics

Page: 318

View: 8466

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During the past forty years, a new trend in the theory of associative algebras, Lie algebras, and their representations has formed under the influence of mathematical logic and universal algebra, namely, the theory of varieties and identities of associative algebras, Lie algebras, and their representations. The last twenty years have seen the creation of the method of 2-words and $\alpha$-functions, which allowed a number of problems in the theory of groups, rings, Lie algebras, and their representations to be solved in a unified way. The possibilities of this method are far from exhausted. This book sums up the applications of the method of 2-words and $\alpha$-functions in the theory of varieties and gives a systematic exposition of contemporary achievements in the theory of identities of algebras and their representations closely related to this method. The aim is to make these topics accessible to a wider group of mathematicians.

Semigroups and Their Applications

Author: Simon M. Goberstein,Peter M. Higgins

Publisher: Springer Science & Business Media

ISBN: 9789027724632

Category: Computers

Page: 211

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Proceedings of the International Conference held at the California State University, Chico, April 10-12, 1986