Groups and Characters / Wiley Series in Pure and Applied Mathematics (PDF)

An authoritative, full-year course on both group theory and
ordinary character theory--essential tools for mathematics and the
physical sciences

One of the few treatments available combining both group theory and
character theory, Groups and Characters is an effective general
textbook on these two fundamentally connected subjects. Presuming
only a basic knowledge of abstract algebra as in a first-year
graduate course, the text opens with a review of background
material and then guides readers carefully through several of the
most important aspects of groups and characters, concentrating
mainly on finite groups.

Challenging yet accessible, Groups and Characters features:

* An extensive collection of examples surveying many different
types of groups, including Sylow subgroups of symmetric groups,
affine groups of fields, the Mathieu groups, and symplectic groups

* A thorough, easy-to-follow discussion of Polya-Redfield
enumeration, with applications to combinatorics

* Inclusive explorations of the transfer function and normal
complements, induction and restriction of characters, Clifford
theory, characters of symmetric and alternating groups, Frobenius
groups, and the Schur index

* Illuminating accounts of several computational aspects of group
theory, such as the Schreier-Sims algorithm, Todd-Coxeter coset
enumeration, and algorithms for generating character tables

As valuable as Groups and Characters will prove as a textbook for
mathematicians, it has broader applications. With chapters suitable
for use as independent review units, along with a full bibliography
and index, it will be a dependable general reference for chemists,
physicists, and crystallographers.