8 Best Books on Representation Theory of Finite Groups

“Representation Theory of Finite Groups” Book Review: This book offers an introductory treatment of the subject, providing an overview of the basic concepts such as group characters, representation modules, and the rectangular representation. It is specifically designed for students seeking an understanding of the topic. The book explores the features of representation theory in the context of rings with identity and finite groups. It also discusses the applications of character theory, accompanied by discussions on classical theorems. The book covers a range of topics, including Group Characters, Representation Modules, Application of Group Theory, Regular Representation, Principal Indecomposable Representations, Radical of a Ring, Semisimple Rings, and more. Numerous exercises and an appendix are included to enhance understanding. This book is recommended for graduate students interested in acquiring knowledge of representation theory.

“Linear Representation of Finite Groups” Book Review: This book is written in a way that is easy for students to understand, and it covers the fundamentals of linear representation of finite groups. It explores how groups can be classified and characterized based on their representation. The book also discusses how each element of a semigroup can be represented by a matrix over a field. It provides a complete classification of representations for a specific class of semigroups. Additionally, the book explores the characteristics of transitive representation and provides examples of transitive representation in finite simple semigroups.

“Representation Theory of Finite Groups: An Introductory Approach” Book Review: This well-designed book offers an introduction to group representation theory, designed for the needs of mature undergraduate students and beginning graduate students. It achieves this by assuming a foundational background in undergraduate linear algebra, group theory, and basic ring theory. The book primarily adopts an approach based on discrete Fourier Analysis, allowing readers to delve into the core concepts of the subject. To demonstrate the practicality of group representation theory, the book provides applications to the spectral theory of graphs. Numerous exercises are included throughout the book, enabling students to apply the theory to real-world problems and enhance their understanding. This book serves as a valuable resource for readers in various disciplines of mathematics and statistics.

“Representation Theory of Finite Groups” Book Review: This well-described book provides a clear and accessible introduction to the Theory of Finite Groups, focusing on several significant breakthroughs within the subject. It serves as an easy-to-read textbook, covering all the essential topics necessary for a comprehensive understanding of the subject matter. The book offers a concise and insightful exposition of the theory of finite groups, incorporating discussions on the theory of modular representations. It discusses various aspects, such as the representation theory of rings with identity, the representation theory of finite groups, applications of character theory, and the construction of irreducible and modular representations. Throughout the book, exercises are included to allow students to assess and reinforce their comprehension of the material.

“Character Theory of Finite Groups” Book Review: This book simplifies the topic in a manner suitable for distance learning, providing a concise solution set for the included problems. The theory discussed in this book has played a crucial role in the classification of finite simple groups. The book begins by introducing the module theory of complex group algebras. With a focus on characters, the material is made more accessible for students, as their needs were a primary consideration during the writing process. To further aid students, a substantial number of challenging problems are included. In addition to covering the fundamental theory, the book also delves into more specialized topics, presenting them in an accessible manner. Topics such as the basics of the Schur index and irreducible character degrees are explored. The book is largely self-contained, requiring readers to possess only the most basic knowledge of linear algebra, group theory, Galois theory, and ring and module theory.

“Representations and Cohomology: Volume 1, Basic Representation Theory of Finite Groups” Book Review: This book offers an accessible course on the subject, catering to both elementary and advanced levels of understanding. It covers all the standard topics while incorporating the perspective of homological algebra and the theory of representations of finite-dimensional algebras. The author places particular emphasis on modular representations and the associated homological algebra. The book provides a self-contained presentation, including the necessary background material. The core of the book is a detailed introduction to the representation theory of finite-dimensional algebras, exploring techniques such as quivers with relations and almost split sequences. This book is highly recommended for students and researchers interested in the study of group theory and algebra.

“A Course in Finite Group Representation Theory” Book Review: This book is a helpful guide that explains the topic in a straightforward manner and shows how it is used in the real world. It is designed for graduate-level students and provides a solid foundation in the representation theory of finite groups over fields and rings. The book covers various important topics such as character tables, induction and restriction, projective and simple modules, and block theory. It includes numerous examples and exercises to test and enhance the reader’s understanding. Prior knowledge of abstract algebra and familiarity with groups, rings, field extensions, and linear algebra is recommended.