Groups and Characters

An authoritative, full-year course on both group theory andordinary character theory--essential tools for mathematics and thephysical sciences One of the few treatments available combining both group theory andcharacter theory, Groups and Characters is an effective generaltextbook on these two fundamentally connected subjects. Presumingonly a basic knowledge of abstract algebra as in a first-yeargraduate course, the text opens with a review of backgroundmaterial and then guides readers carefully through several of themost important aspects of groups and characters, concentratingmainly on finite groups. Challenging yet accessible, Groups and Characters features: * An extensive collection of examples surveying many differenttypes 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-Redfieldenumeration, with applications to combinatorics * Inclusive explorations of the transfer function and normalcomplements, induction and restriction of characters, Cliffordtheory, characters of symmetric and alternating groups, Frobeniusgroups, and the Schur index * Illuminating accounts of several computational aspects of grouptheory, such as the Schreier-Sims algorithm, Todd-Coxeter cosetenumeration, and algorithms for generating character tables As valuable as Groups and Characters will prove as a textbook formathematicians, it has broader applications. With chapters suitablefor use as independent review units, along with a full bibliographyand index, it will be a dependable general reference for chemists,physicists, and crystallographers.