The Restricted Burnside Problem [Hardcover]

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. This popular 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 on Zelmanov'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.

Preface
Contents
Notation
1. Basic Concepts
2. The Associated Lie Ring of a Group
3. Kostrikin's Theorem
4. Razmyslov's Theorem
5. Groups of Exponent Two, Three, and Six
6. Groups of Exponent Four
7. Groups of Prime Exponent
8. Groups of Prime-power Exponent
9. Zelmanov's Theorem
Appendix A
Appendix B
Index