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An Introduction to the Theory of Groups (4E) by Joseph Rotman
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About this book :-
An Introduction to the Theory of Groups (4E) written by Joseph Rotman
This books is valuable text, 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. 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).
Book Detail :-
Title: An Introduction to the Theory of Groups
Edition: Fourth Edition
Author(s): Joseph Rotman
Publisher: Springer-Verlag New York
Series: Graduate Texts in Mathematics
ISBN: 978-1-4612-8686-8, 978-1-4612-4176-8
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Book Contents :-
An Introduction to the Theory of Groups (4E) written by Joseph Rotman cover the following topics.
1. Groups and Homomorphisms
2. The Isomorphism Theorems 20
3. Symmetric Groups and G-Sets
4. The Sylow Theorems
5. Normal Series
6. Finite Direct Products
7. Extensions and Cohomology
8. Some Simple Linear Groups
9. Permutations and the Mathieu Groups
10. Abelian Groups
11. Free Groups and Free Products
12. The Word Problem
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
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