**Graduate Studies in Mathematics**

Volume: 92;
2008;
350 pp;
Hardcover

MSC: Primary 20;

Print ISBN: 978-0-8218-4344-4

Product Code: GSM/92

List Price: $65.00

Individual Member Price: $52.00

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

List Price: $65.00

Individual Member Price: $52.00

#### 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.

#### 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

#### Readership

Graduate students interested in group theory.

#### 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.

`CHEL/359.H`

`CHEL/301.H`

```
CHEL/288.H
```

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.

`CHEL/359.H`

`CHEL/301.H`

```
CHEL/288.H
```

-- MAA Reviews