Softcover ISBN:  9781470471606 
Product Code:  GSM/92.S 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
eBook ISBN:  9781470411602 
Product Code:  GSM/92.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470471606 
eBook: ISBN:  9781470411602 
Product Code:  GSM/92.S.B 
List Price:  $174.00 $131.50 
MAA Member Price:  $156.60 $118.35 
AMS Member Price:  $139.20 $105.20 
Softcover ISBN:  9781470471606 
Product Code:  GSM/92.S 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
eBook ISBN:  9781470411602 
Product Code:  GSM/92.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470471606 
eBook ISBN:  9781470411602 
Product Code:  GSM/92.S.B 
List Price:  $174.00 $131.50 
MAA Member Price:  $156.60 $118.35 
AMS Member Price:  $139.20 $105.20 

Book DetailsGraduate Studies in MathematicsVolume: 92; 2008; 350 ppMSC: Primary 20;
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 Jsubgroup and his normal \(p\)complement theorem.
Topics that seldom (or never) appear in books are also covered. These include subnormality theory, a grouptheoretic 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 Pólya Lecturer in 2003–2005.ReadershipGraduate students interested in group theory.

Table of Contents

Chapters

Chapter 1. Sylow theory

Chapter 2. Subnormality

Chapter 3. Split extensions

Chapter 4. Commutators

Chapter 5. Transfer

Chapter 6. Frobenius actions

Chapter 7. The Thompson subgroup

Chapter 8. Permutation groups

Chapter 9. More on subnormality

Chapter 10. More transfer theory

Chapter 11. The basics


Additional Material

Reviews

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


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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 Jsubgroup and his normal \(p\)complement theorem.
Topics that seldom (or never) appear in books are also covered. These include subnormality theory, a grouptheoretic 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 Pólya Lecturer in 2003–2005.
Graduate students interested in group theory.

Chapters

Chapter 1. Sylow theory

Chapter 2. Subnormality

Chapter 3. Split extensions

Chapter 4. Commutators

Chapter 5. Transfer

Chapter 6. Frobenius actions

Chapter 7. The Thompson subgroup

Chapter 8. Permutation groups

Chapter 9. More on subnormality

Chapter 10. More transfer theory

Chapter 11. The basics

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