A Course in the Theory of Groups

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Overview

A Course in the Theory of Groups is a comprehensive introduction to the theory of groups - finite and infinite, commutative and non-commutative. Presupposing only a basic knowledge of modern algebra, it introduces the reader to the different branches of group theory and to its principal accomplishments. While stressing the unity of group theory, the book also draws attention to connections with other areas of algebra such as ring theory and homological algebra.
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Acceptable Used-Acceptable. Ships from UK in 48 hours or less (usually same day). Your purchase helps support the African Children's Educational Trust (A-CET). Ex-library with ... wear and barcode page may have been removed. 100% money back guarantee. We are a world class secondhand bookstore based in Hertfordshire, United Kingdom and specialize in high quality textbooks across an enormous variety of subjects. We aim to provide a vast range of textbooks, rare and collectible books at a great price. Through our work with A-CET we have helped give hundreds of young people in Africa the vital chance to get an education. We provide a 100% money back guarantee and are dedicated to providing our customers with the highest standards of service in the bookselling industry. *****PLEASE NOTE: This item is shipping from an authorized seller in Europe. In the event that a return is necessary, you will be able to return your item within the US. To learn more about our European sellers and policies see the BookQuest FAQ Read more Show Less

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More About This Book

Overview

A Course in the Theory of Groups is a comprehensive introduction to the theory of groups - finite and infinite, commutative and non-commutative. Presupposing only a basic knowledge of modern algebra, it introduces the reader to the different branches of group theory and to its principal accomplishments. While stressing the unity of group theory, the book also draws attention to connections with other areas of algebra such as ring theory and homological algebra.
This new edition has been updated at various points, some proofs have been improved, and lastly about thirty additional exercises are included. There are three main additions to the book. In the chapter on group extensions an exposition of Schreier's concrete approach via factor sets is given before the introduction of covering groups. This seems to be desirable on pedagogical grounds. Then S. Thomas's elegant proof of the automorphism tower theorem is included in the section on complete groups. Finally an elementary counterexample to the Burnside problem due to N.D. Gupta has been added in the chapter on finiteness properties.
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Product Details

Table of Contents

Preface to the Second Edition
Preface to the First Edition
Notation
Ch. 1 Fundamental Concepts of Group Theory 1
Ch. 2 Free Groups and Presentations 44
Ch. 3 Decompositions of a Group 63
Ch. 4 Abelian Groups 93
Ch. 5 Soluble and Nilpotent Groups 121
Ch. 6 Free Groups and Free Products 159
Ch. 7 Finite Permutation Groups 192
Ch. 8 Representations of Groups 213
Ch. 9 Finite Soluble Groups 252
Ch. 10 The Transfer and Its Applications 285
Ch. 11 The Theory of Group Extensions 310
Ch. 12 Generalizations of Nilpotent and Soluble Groups 356
Ch. 13 Subnormal Subgroups 385
Ch. 14 Finiteness Properties 416
Ch. 15 Infinite Soluble Groups 450
Bibliography 479
Index 491
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Customer Reviews

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  • Anonymous

    Posted November 22, 2001

    very good, but not the best

    The author's selection of material is extremely good. Many details in proofs are omitted, so, this book is very demanding on the reader. A graduate level course in algebra is a must before reading this book. Exercises are good, many of them quite tricky and challanging. Overall, a very good reference book for those interested in research in group theory.

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  • Anonymous

    Posted April 11, 2001

    nice book

    interesting group theory book which has a nice section on permutation groups.

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  • Anonymous

    Posted November 19, 2008

    No text was provided for this review.

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