Groups and Characters: 1st Edition (Paperback) book cover

Groups and Characters

1st Edition

By Victor E Hill

Chapman and Hall/CRC

239 pages

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pub: 1999-11-22
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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.


"…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

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.

Subject Categories

BISAC Subject Codes/Headings: