**Graduate Studies in Mathematics**

Volume: 92;
2008;
350 pp;
Softcover

MSC: Primary 20;

**Print ISBN: 978-1-4704-7160-6
Product Code: GSM/92.S**

List Price: $69.00

AMS Member Price: $55.20

MAA Member Price: $62.10

**Electronic ISBN: 978-1-4704-1160-2
Product Code: GSM/92.E**

List Price: $65.00

AMS Member Price: $52.00

MAA Member Price: $58.50

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#### Supplemental Materials

# Finite Group Theory

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*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 Pólya Lecturer in 2003–2005.

#### Readership

Graduate students interested in group theory.

#### Reviews & Endorsements

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

#### Table of Contents

# Table of Contents

## Finite Group Theory

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents vii8 free
- Preface ix10 free
- Chapter 1. Sylow Theory 114 free
- Chapter 2. Subnormality 4558
- Chapter 3. Split Extensions 6578
- Chapter 4. Commutators 113126
- Chapter 5. Transfer 147160
- Chapter 6. Frobenius Actions 177190
- Chapter 7. The Thompson Subgroup 201214
- Chapter 8. Permutation Groups 223236
- Chapter 9. More on Subnormality 271284
- Chapter 10. More Transfer Theory 295308
- Appendix: The Basics 325338
- Index 345358
- Errata 351364
- Back Cover Back Cover1368