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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
** Year: ** 1995
** Pages: ** 529
** Type: ** PDF
** Language: ** English
** ISBN: ** 978-1-4612-8686-8, 978-1-4612-4176-8
** Country: ** US

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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

Bibliography

Notation

Index

**Note:-**

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