Customer Reviews

An Introduction to the Theory of Groups

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I used this book as a means of writing my senior thesis on the clasification of the projective unimodular groups and the Mathieu groups as being simple. Most of the proofs were well constructed and easy to follow. What this books lacks is a proof reading. Several of the proofs make no sense in the form in which they are written. Also, his notation at times becomes cluttered and not easy to follow. One can imagine how difficult notation can be in general, but when it is full of typographical errors, it can be almost impossible to wade through without the help of someone who knows the material. This book is certainly not a waste of time to read and is very good as a reference for theorems concerning finite groups, however do not put all your eggs in one basket and base your education on this one book.

This is a good book, well-organized and contains many useful materials. However I do not recommend it as an independent study textbook (which is what I did). There are many errors, most of them are typographical but some of them are wrong numbers which are very difficult to correct, especially in the exercises given. And the exercises are very important -- the following discussions and proofs depend on some of them. Springer published a "corrected second printing" in 1999 but obviously they didn't do a good job (I purchased the new one and I got the old one in the library).

I am not sure I would take this specific book to a desert island but I would highly recommend it to anyone who is in possession of patience, self-motivation and willingness to spend time working through both the problems and any gaps that may occur within the proofs. This book can be used both by Graduate students or as a topics/independent study course for well prepared and motivated undergraduates.
In general, you can be guaranteed that the exposition present within any book by Rotman is par-excellence and this book is no exception. The material is presented in a sound and definite logical manner, which results in gently directing the reader through an 'introduction' to group theory by presenting the material in well thought out and bite sized portions. The only negative aspect of this book, which is minimal as best, is the authors choice of notation, for example the notation used to define G-sets in chapter 3 does not necessarily do the topic justice since G-sets in their own right are an important concept. But, as stated, this is the only complaint and is easily remedied. Enjoy!

This is one of the most interesting math books I've ever read- probably one of those I'd take with me on a desert island, if I ever need math books on a desert island! ;) It is a solid introduction to group theory, beginning with symmetric groups; it includes quite a lot of things about finite groups, solvable and nilpotent groups, permutation groups, free groups and combinatorial group theory (with interesting parts about the word problem), etc. Rotman's style is very pleasant to read.

My second abstract algebra class had no lecture notes, and the textbook was Robinson's A Course in the Theory of Groups. I couldn't get through even the first chapter of this book, so my professor recommended that I read this book by Rotman instead. The structure of things in algebra started making much more sense to me. I was able to understand much better what was going on in class and the motivation for what we studied. Though it's self-contained, I'd recommend this as a book for self-study once you've already got a handle on the basics of algebra. The exercises are tricky but doable, and the way the book is structured, it is essential to read them to understand the arguments. Some proofs depend on solutions to exercises.

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.

However some minor bugs are still present in the fourth edition, but nothing serious.