Description

Book Synopsis
The aim of this text is to present some of the key results in the representation theory of finite groups. In order to keep the account reasonably elementary, so that it can be used for graduate-level courses, Professor Alperin has concentrated on local representation theory, emphasising module theory throughout. In this way many deep results can be obtained rather quickly. After two introductory chapters, the basic results of Green are proved, which in turn lead in due course to Brauer's First Main Theorem. A proof of the module form of Brauer's Second Main Theorem is then presented, followed by a discussion of Feit's work connecting maps and the Green correspondence. The work concludes with a treatment, new in part, of the Brauer-Dade theory. As a text, this book contains ample material for a one semester course. Exercises are provided at the end of most sections; the results of some are used later in the text. Representation theory is applied in number theory, combinatorics and in ma

Trade Review
'… a beautifully written book. Anyone wishing to learn the fundamental facts of Brauer's theory of blocks cannot do better than to begin his study with this text.' Bulletin of the London Mathematical Society

Table of Contents
Preface; Part I. Semi-Simple Modules: Part II. Projective Modules: Part III. Modules and Subgroups: Part IV. Blocks: Part V. Cyclic Blocks.

Local Representation Theory Modular Representations as an Introduction to the Local Representation Theory of Finite Groups 11 Cambridge Studies in Advanced Mathematics Series Number 11

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    A Paperback by J. L. Alperin

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      View other formats and editions of Local Representation Theory Modular Representations as an Introduction to the Local Representation Theory of Finite Groups 11 Cambridge Studies in Advanced Mathematics Series Number 11 by J. L. Alperin

      Publisher: Cambridge University Press
      Publication Date: 9/24/1993 12:00:00 AM
      ISBN13: 9780521449267, 978-0521449267
      ISBN10: 052144926X
      Also in:
      Groups and group theory

      Description

      Book Synopsis
      The aim of this text is to present some of the key results in the representation theory of finite groups. In order to keep the account reasonably elementary, so that it can be used for graduate-level courses, Professor Alperin has concentrated on local representation theory, emphasising module theory throughout. In this way many deep results can be obtained rather quickly. After two introductory chapters, the basic results of Green are proved, which in turn lead in due course to Brauer's First Main Theorem. A proof of the module form of Brauer's Second Main Theorem is then presented, followed by a discussion of Feit's work connecting maps and the Green correspondence. The work concludes with a treatment, new in part, of the Brauer-Dade theory. As a text, this book contains ample material for a one semester course. Exercises are provided at the end of most sections; the results of some are used later in the text. Representation theory is applied in number theory, combinatorics and in ma

      Trade Review
      '… a beautifully written book. Anyone wishing to learn the fundamental facts of Brauer's theory of blocks cannot do better than to begin his study with this text.' Bulletin of the London Mathematical Society

      Table of Contents
      Preface; Part I. Semi-Simple Modules: Part II. Projective Modules: Part III. Modules and Subgroups: Part IV. Blocks: Part V. Cyclic Blocks.

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