By I. Martin Isaacs
Character conception presents a strong instrument for proving theorems approximately finite teams. as well as facing ideas for making use of characters to "pure" staff concept, a wide a part of this ebook is dedicated to the homes of the characters themselves and the way those houses mirror and are mirrored within the constitution of the group.
Chapter I involves ring theoretic preliminaries. Chapters 2 to six and eight include the elemental fabric of personality idea, whereas bankruptcy 7 treats a tremendous approach for the applying of characters to staff conception. bankruptcy nine considers irreducible representations over arbitrary fields, resulting in a spotlight on subfields of the complicated numbers in bankruptcy 10. In bankruptcy 15 the writer introduces Brauer’s idea of blocks and "modular characters." last chapters care for extra really expert themes, akin to the connections among the set of levels of the irreducible characters and constitution of a gaggle. Following every one bankruptcy is a variety of conscientiously concept out difficulties, together with workouts, examples, additional effects and extensions and adaptations of theorems within the text.
Prerequisites for this ebook are a few uncomplicated finite workforce conception: the Sylow theorems, common homes of permutation teams and solvable and nilpotent teams. additionally necessary will be a few familiarity with jewelry and Galois thought. in brief, the contents of a first-year graduate algebra direction might be enough preparation.
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