Finite Group Theory (Graduate Studies in Mathematics) by I.Martin Isaacs

by I. Martin Isaacs

The text begins with a review of group actions and Sylow theory. It includes semidirect products, the Schur-Zassenhaus theorem, the theory of commutators, coprime actions on groups, transfer theory, Frobenius groups, primitive and multiply transitive permutation groups, the simplicity of the PSL groups, the generalized Fitting subgroup and also Thompson's J-subgroup and his normal $p$-complement theorem. Topics that seldom (or never) appear in books are also covered. These include subnormality theory, a group-theoretic proof of Burnside's theorem about groups with order divisible by just two primes, the Wielandt automorphism tower theorem, Yoshida's transfer theorem, the ``principal ideal theorem'' of transfer theory and many smaller results that are not very well known. Proofs often contain original ideas, and they are given in complete detail. In many cases they are simpler than can be found elsewhere. The book is largely based on the author's lectures, and consequently, the style is friendly and somewhat informal. Finally, the book includes a large collection of problems at disparate levels of difficulty. These should enable students to practice group theory and not just read about it. Martin Isaacs is professor of mathematics at the University of Wisconsin, Madison. Over the years, he has received many teaching awards and is well known for his inspiring teaching and lecturing. He received the University of Wisconsin Distinguished Teaching Award in 1985, the Benjamin Smith Reynolds Teaching Award in 1989, and the Wisconsin Section MAA Teaching Award in 1993, to name only a few. He was also honored by being the selected MAA Polya Lecturer in 2003-2005.

Genres: Mathematics

Hardcover

First published August 6, 2008

About the author

Irving Martin Isaacs

Reviews

[Steve Dalton · Rating 5 out of 5]

I read this book for the first time several years ago. I read it again about 18 months ago. I plan to read it once again during the upcoming summer break, and I'll probably do a "full" review then.

But for now, I wanted to note that this is the best math book I have ever read. It excels on all levels, and truly is a work of art. I learned so much from this book, and came to appreciate finite group theory even more after I had finished reading it. It is filled with gems, and is in every way a treat for the reader. It is the only math book I can think of which I've gone back and reread - not out of necessity - but out of true pleasure. If all math books were written by Isaacs, we'd have too many mathematicians!

If you have any interest at all in finite group theory, and have a little bit of mathematical sophistication, read (and re-read) this book. You'll find lots of topics here that are not treated in any "intro" course, yet they'll be easier to understand than almost anything at the "intro" level. The exercises will challenge you greatly, but it is so rewarding to do them (and redo them). You'll come out of this book with a respect for finite group theory as an interesting and inviting subject, and a respect for Isaacs as a supremely talented mathematical expositor.

[Chris · Rating 5 out of 5]

If you have squishy feelings about the beauty and elegance of finite group theory, you will enjoy this book. The text is insightful and self-contained. The problems can be challenging but never crushingly so, and hence they are incredibly rewarding. After reading, I'm not sure if I wish I were a group theorist or simply friends with Marty Isaacs...

[Sourav Mandal · Rating 4 out of 5]

Best book