Introduction to the Theory of Groups

ISBN-10: 0387942858
ISBN-13: 9780387942858
Edition: 4th 1995 (Revised)
Authors: Joseph J. Rotman
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Description: 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  More...

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Book details

Edition: 4th
Copyright year: 1995
Publisher: Springer
Publication date: 8/13/1999
Binding: Hardcover
Pages: 517
Size: 6.25" wide x 9.50" long x 0.75" tall
Weight: 2.2
Language: English

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).

Preface to the Fourth Edition
From Preface to the Third Edition
To the Reader
Groups and Homomorphisms
The Isomorphism Theorems
Symmetric Groups and G-Sets
The Sylow Theorems
Normal Series
Finite Direct Products
Extensions and Cohomology
Some Simple Linear Groups
Permutations and the Mathieu Groups
Abelian Groups
Free Groups and Free Products
The Word Problem
Epilogue
Appendix I: Some Major Algebraic Systems
Appendix II: Equivalence Relations and Equivalence Classes
Appendix III: Functions
Appendix IV: Zorn's Lemma
Appendix V: Countability
Appendix VI: Commutative Rings
Bibliography
Notation
Index

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