Groups and Characters  book cover
1st Edition

Groups and Characters

ISBN 9781584880387
Published November 22, 1999 by Chapman and Hall/CRC
239 Pages

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Book Description

Group representation theory is both elegant and practical, with important applications to quantum mechanics, spectroscopy, crystallography, and other fields in the physical sciences. Until now, however, there have been virtually no accessible treatments of group theory that include representations and characters. The classic works in the field require a high level of mathematical sophistication, and other texts omit representations and characters.

Groups and Characters offers an easy-to-follow introduction to the theory of groups and of group characters. Designed as a rapid survey of the subject, this unique text emphasizes examples and applications of the theorems, and avoids many of the longer and more difficult proofs. The author presents group theory through the Sylow Theorems and includes the full subgroup structure of A5. Representations and characters are worked out with numerous character tables, along with real and induced characters that lead to the table for S5.

The text includes specific sections that provide the mathematical basis for some of the important applications of group theory in spectroscopy and molecular structure. It also offers numerous exercises-some stressing computation of concrete examples, others stressing development of the mathematical theory.

Groups and Characters provides the ideal grounding for more advanced studies with the classic texts, and for more broad-based work in abstract algebra. Furthermore, physical scientists-whose experience with groups and characters may not be rigorous-will find Groups and Characters the ideal means for gaining a sense of the mathematics lying behind the techniques used in applications.

Table of Contents

Introductory Examples
Groups and Subgroups
Point Groups and Cosets
Homomorphisms and Normal Subgroups
Isomorphisms and Automorphisms
Factor Groups
Sylow Subgroups
Permutation Groups
Matrix Groups
Group Representations
Regular Representations
Irreducible Representations
Representations of Abelian Groups
Group Characters
Orthogonality Relations and Character Tables
Reducible Characters
The Burnside Counting Theorem
Real Characters
Induced Representations and Characters
The Character Table for S5
Space Groups and Semi-Direct Products
Proofs of the Sylow Theorems
Index of Symbols.

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"…rigorous and appropriate…excellent starting point for anyone interested in the theory of groups, representations and characters. Upper division undergraduates through professionals."
-D. S. Larson, Gonzago University in CHOICE