Finite Group Theory (Graduate Studies in Mathematics, Vol. 92) 1st Edition by I. Martin Isaacs (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review “As might be expected from a book by Isaacs, although the topics are familiar, almost every chapter contains unexpected gems not to be found in most basic textbooks. Surely many readers will be inspired by this book to continue their study of the fascinating field of finite group theory.” —- Mathematical Reviews”This is one serious group theory book, intended for graduate students with strong algebra backgrounds who plan to read papers on group theory after this course. Each chapter comes with a freight car full of substantial exercises, ranging in difficulty from trivial to research level. If you’re studying group theory anytime soon get a copy.” —- MAA Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I own this book for more than 5 years and I used it on my graduate studies, I am working on Finite Group theory. This book is for people who interested in the study of group theory.

⭐I used this for a graduate course and enjoyed it quite a bit. Isaacs is a decent writer.

⭐Every book written by Isaacs is very nice!

⭐Excellent intermediate text on finite groups excluding representation theory. The proofs are succinct and insightful but better still, the motivation for the development of the subject is clear and engaging. Covers similar material to The Theory of Finite Groups: An Introduction (Universitext) by Hans Kurzweil and Bernd Stellmacher but it is well worth having both.

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