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An Introduction to the Theory of Groups : Graduate Texts in Mathematics - Joseph J. Rotman

An Introduction to the Theory of Groups

Graduate Texts in Mathematics

Hardcover Published: 1st September 1999
ISBN: 9780387942858
Number Of Pages: 517

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Anyone who has studied "abstract algebra" and linear algebra as an undergraduate can understand this book. This edition has been completely revised and reorganized, without however losing any of the clarity of presentation that was the hallmark of the previous editions.
The first six chapters provide ample material for a first course: beginning with the basic properties of groups and homomorphisms, topics covered include Lagrange's theorem, the Noether isomorphism theorems, symmetric groups, "G"-sets, the Sylow theorems, finite Abelian groups, the Krull-Schmidt theorem, solvable and nilpotent groups, and the Jordan-Holder theorem.
The middle portion of the book uses the Jordan-Holder theorem to organize the discussion of extensions (automorphism groups, semidirect products, the Schur-Zassenhaus lemma, Schur multipliers) and simple groups (simplicity of projective unimodular groups and, after a return to "G"-sets, a construction of the sporadic Mathieu groups).

Industry Reviews

Fourth Edition

J.J. Rotman

An Introduction to the Theory of Groups

"Rotman has given us a very readable and valuable text, and has shown us many beautiful vistas along his chosen route."-MATHEMATICAL REVIEWS

Preface to the Fourth Edition
From Preface to the Third Edition
To the Reader
Groups and Homomorphismsp. 1
The Isomorphism Theoremsp. 20
Symmetric Groups and G-Setsp. 43
The Sylow Theoremsp. 73
Normal Seriesp. 89
Finite Direct Productsp. 125
Extensions and Cohomologyp. 154
Some Simple Linear Groupsp. 217
Permutations and the Mathieu Groupsp. 247
Abelian Groupsp. 307
Free Groups and Free Productsp. 343
The Word Problemp. 418
Epiloguep. 471
Appendix I: Some Major Algebraic Systemsp. 475
Appendix II: Equivalence Relations and Equivalence Classesp. 477
Appendix III: Functionsp. 479
Appendix IV: Zorn's Lemmap. 481
Appendix V: Countabilityp. 483
Appendix VI: Commutative Ringsp. 485
Bibliographyp. 495
Notationp. 498
Indexp. 503
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387942858
ISBN-10: 0387942858
Series: Graduate Texts in Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 517
Published: 1st September 1999
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 1.91
Weight (kg): 0.93
Edition Number: 4
Edition Type: Revised

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