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A Course in Finite Group Representation Theory
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Book description

This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.

Reviews

'This is a well-written and motivated book, with carefully chosen topics, examples and exercises to engage the reader, making it suitable in the classroom or for self-study.'

Felipe Zaldivar Source: MAA Reviews

'The author aims to provide a comprehensive but fastpaced grounding in results which can be applied to areas as diverse as number theory, combinatorics, topology or commutative algebra … While the proofs are rigorous, the style is relatively informal and designed to showcase as many results as possible which are applicable beyond the realms of \"pure representation theory.'

Stuart Martin Source: MathSciNet

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Contents

Bibliography
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[21] J., Thévenaz, G-Algebras and modular representation theory, Oxford University Press, Oxford, 1995.

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