Representations and Characters of Finite Groups [Paperback]

Representation theory and character theory have proved essential in the study of finite simple groups since their early development by Frobenius.Representation theory and character theory have proved essential in the study of finite simple groups since their early development by Frobenius. The author begins by presenting the foundations of character theory in a style accessible to advanced undergraduates requiring only a basic knowledge of group theory and general algebra.Representation theory and character theory have proved essential in the study of finite simple groups since their early development by Frobenius. The author begins by presenting the foundations of character theory in a style accessible to advanced undergraduates requiring only a basic knowledge of group theory and general algebra.Representation theory and character theory have proved essential in the study of finite simple groups since their early development by Frobenius. The author begins by presenting the foundations of character theory in a style accessible to advanced undergraduates that requires only a basic knowledge of group theory and general algebra. This theme is then expanded in a self-contained account providing an introduction to the application of character theory to the classification of simple groups. The book follows both strands of the theory: the exceptional characteristics of Suzuki and Feit and the block character theory of Brauer and includes refinements of original proofs that have become available as the subject has grown.Preface; 1. General representation theory; 2. Complex characters; 3. Suzuki's theory of exceptional characters; 4. Coherence and exceptional characters; 5. The characterisation of characters; 6. Isometries; Appendix: Glauberman's Z*-theorem; References; Index of notation; Index. The value of this book lies not in its encyclopedic approach to the subject...nor in its plethora of examples--the text is written concisely. The text's greatest attraction lielÃ&