The Restricted Burnside Problem

by Vaughan-Lee, Michael

• ISBN13: 9780198535737
• ISBN10: 0198535732
• Format: Hardcover
• Copyright: 1990-03-22
• Publisher: Oxford University Press

Summary

In 1902 William Burnside wrote "A still undecided point in the theory of discontinuous groups is whether the order of a group may not be finite while the order of every operation it contains is finite." Since then, the Burnside problem has inspired a considerable amount of research. Thispopular text provides a comprehensive account of the many recent results obtained in studies of the restricted Burnside problem by making extensive use of Lie ring techniques that provide for a uniform treatment of the field. The updated and revised second edition includes a new chapter onZelmanov's highly acclaimed, recent solution to the restricted Burnside problem for arbitrary prime-power exponents. Much of the material presented has until now been available only in Russian journals. This book will be welcomed by researchers and students in group theory.

Table of Contents

Preface

Contents

Notation

Basic Concepts

The Associated Lie Ring of a Group

Kostrikin's Theorem

Razmyslov's Theorem

Groups of Exponent Two, Three, and Six

Groups of Exponent Four

Groups of Prime Exponent

Groups of Prime-power Exponent

Zelmanov's Theorem

Appendix A

Appendix B

Index

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