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Group Theory

Group Theory Author W. R. Scott
ISBN-10 9780486140162
Release 2012-05-23
Pages 512
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Here is clear, well-organized coverage of the most standard theorems, including isomorphism theorems, transformations and subgroups, direct sums, abelian groups, and more. This undergraduate-level text features more than 500 exercises.

Character Theory of Finite Groups

Character Theory of Finite Groups Author I. Martin Isaacs
ISBN-10 0486680142
Release 1994
Pages 303
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"The book is a pleasure to read. There is no question but that it will become, and deserves to be, a widely used textbook and reference." — Bulletin of the American Mathematical Society. Character theory provides a powerful tool for proving theorems about finite groups. In addition to dealing with techniques for applying characters to "pure" group theory, a large part of this book is devoted to the properties of the characters themselves and how these properties reflect and are reflected in the structure of the group. Chapter I consists of ring theoretic preliminaries. Chapters 2 to 6 and 8 contain the basic material of character theory, while Chapter 7 treats an important technique for the application of characters to group theory. Chapter 9 considers irreducible representations over arbitrary fields, leading to a focus on subfields of the complex numbers in Chapter 10. In Chapter 15 the author introduces Brauer’s theory of blocks and "modular characters." Remaining chapters deal with more specialized topics, such as the connections between the set of degrees of the irreducible characters and structure of a group. Following each chapter is a selection of carefully thought out problems, including exercises, examples, further results and extensions and variations of theorems in the text. Prerequisites for this book are some basic finite group theory: the Sylow theorems, elementary properties of permutation groups and solvable and nilpotent groups. Also useful would be some familiarity with rings and Galois theory. In short, the contents of a first-year graduate algebra course should be sufficient preparation.

Theory of Continuous Groups

Theory of Continuous Groups Author Charles Loewner
ISBN-10 9780486462929
Release 2008-02
Pages 110
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Based on lectures by a renowned educator, this book focuses on continuous groups, particularly in terms of applications in geometry and analysis. The author's unique perspectives are illustrated by numerous inventive geometric examples, many of which were inspired by footnotes among the work of Sophus Lie. 1971 edition.

An Introduction to the Theory of Groups

An Introduction to the Theory of Groups Author Pavel Sergeevich Aleksandrov
ISBN-10 OCLC:4528616
Release 1965
Pages 112
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An Introduction to the Theory of Groups has been writing in one form or another for most of life. You can find so many inspiration from An Introduction to the Theory of Groups also informative, and entertaining. Click DOWNLOAD or Read Online button to get full An Introduction to the Theory of Groups book for free.

Problems in Group Theory

Problems in Group Theory Author John D. Dixon
ISBN-10 9780486459165
Release 2007-01
Pages 176
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265 challenging problems in all phases of group theory, gathered for the most part from papers published since 1950, although some classics are included.

A Course on Group Theory

A Course on Group Theory Author John S. Rose
ISBN-10 9780486170664
Release 2013-05-27
Pages 320
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Text for advanced courses in group theory focuses on finite groups, with emphasis on group actions. Explores normal and arithmetical structures of groups as well as applications. 679 exercises. 1978 edition.

Representation Theory of Finite Groups

Representation Theory of Finite Groups Author Martin Burrow
ISBN-10 9780486674872
Release 1965
Pages 185
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Concise, graduate-level exposition of the theory of finite groups, including the theory of modular representations. Topics include representation theory of rings with identity, representation theory of finite groups, applications of the theory of characters, construction of irreducible representations and modular representations. Rudiments of linear algebra and knowledge of group theory helpful prerequisites. Exercises. Bibliography. Appendix. 1965 edition.

The Theory of Groups and Quantum Mechanics

The Theory of Groups and Quantum Mechanics Author Hermann Weyl
ISBN-10 0486602699
Release 1950
Pages 422
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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.

The Theory of Groups

The Theory of Groups Author Marshall Hall
ISBN-10 9780486816906
Release 2018-02-15
Pages 448
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This 1959 text offers an unsurpassed resource for learning and reviewing the basics of a fundamental and ever-expanding area. "This remarkable book undoubtedly will become a standard text on group theory." — American Scientist.

Groups Rings Modules

Groups  Rings  Modules Author Maurice Auslander
ISBN-10 9780486795423
Release 2014-06-01
Pages 480
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Classic monograph covers sets and maps, monoids and groups, unique factorization domains, localization and tensor products, applications of fundamental theorem, algebraic field extension, Dedekind domains, and much more. 1974 edition.

A Course in the Theory of Groups

A Course in the Theory of Groups Author Derek Robinson
ISBN-10 9781468401288
Release 2012-12-06
Pages 481
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" 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.

Group Theory and Chemistry

Group Theory and Chemistry Author David M. Bishop
ISBN-10 9780486132327
Release 2012-07-12
Pages 336
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Concise, self-contained introduction to group theory and its applications to chemical problems. Symmetry, matrices, molecular vibrations, transition metal chemistry, more. Relevant math included. Advanced-undergraduate/graduate-level. 1973 edition.

Permutation Groups

Permutation Groups Author Donald S. Passman
ISBN-10 9780486310916
Release 2013-10-03
Pages 160
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Lecture notes by a prominent authority provide a self-contained account of classification theorems. Includes work of Zassenhaus on Frobenius elements and sharply transitive groups, Huppert's theorem, more. 1968 edition.

Group Theory and Its Application to Physical Problems

Group Theory and Its Application to Physical Problems Author Morton Hamermesh
ISBN-10 9780486140391
Release 2012-04-26
Pages 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.


Symmetry Author R. McWeeny
ISBN-10 9781483226248
Release 2013-09-03
Pages 262
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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.

Rotations Quaternions and Double Groups

Rotations  Quaternions  and Double Groups Author Simon L. Altmann
ISBN-10 9780486317731
Release 2013-04-09
Pages 336
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This self-contained text presents a consistent description of the geometric and quaternionic treatment of rotation operators, employing methods that lead to a rigorous formulation and offering complete solutions to many illustrative problems. Geared toward upper-level undergraduates and graduate students, the book begins with chapters covering the fundamentals of symmetries, matrices, and groups, and it presents a primer on rotations and rotation matrices. Subsequent chapters explore rotations and angular momentum, tensor bases, the bilinear transformation, projective representations, and the geometry, topology, and algebra of rotations. Some familiarity with the basics of group theory is assumed, but the text assists students in developing the requisite mathematical tools as necessary.

Lie Groups Lie Algebras and Some of Their Applications

Lie Groups  Lie Algebras  and Some of Their Applications Author Robert Gilmore
ISBN-10 9780486131566
Release 2012-05-23
Pages 608
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This text introduces upper-level undergraduates to Lie group theory and physical applications. It further illustrates Lie group theory's role in several fields of physics. 1974 edition. Includes 75 figures and 17 tables, exercises and problems.