An Introduction to the Theory of Groups

Graduate Texts in Mathematics #148

by Joseph J. Rotman

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).

Genres: Mathematics, Science, Theory, Textbooks, Algebra

500 pages, Hardcover

First published January 1, 1984

Reviews

[Mark Moon]

Wonderful, but a little terse. I enjoyed the material on Mathieu groups, fundamental groups of simplicial complexes, and the word problem for groups. Suitable for a ~3rd course in group theory.

[Nada]

I learned the basic information about group theory: groups, Isomorphism theorems, permutation groups, Sylow theorems, Normal series, solvable, supersolvable, nilpotent and so on...

[Babak]

Reading this book was an entertainment for me :] Since it is only about groups, it introduces many elegant theorems and corollaries in its text and its exercises.

[Ayush Bhat]

Starting slowly, this book is very good for everyone who want to self study seriously group theory. This is by far the best book I have on this subject. The difficulty is very gradual and there is a real dedication of the author to make understand the concepts to the reader. A very good book, easy to read in the first chapters, less in the last.

[LM]

...one must always salivate, like Pavlov's dog, by asking for its kernel and image...