Michael Vaughan-Lee

The Restricted Burnside Problem

• Gebundenes Buch

Produktbeschreibung

The first edition of this book provided an account of the restricted Burnside problem making extensive use of Lie ring techniques to provide a uniform treatment of the field. It also included Kostrikin's theorem for groups of prime exponent. The second edition, as well as providing general updating, contains a new chapter on E.I. Zelmanov's highly acclaimed and recent solution to the Restricted Burnside Problem for arbitrary prime-power exponent. This material is currently only available in papers in Russian journals. This proof of Zelmanov's theorem given in the new edition is self contained, and (unlike Zelmanov's original proof) does not rely on the theory of Jordan algebras.

---

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.

Produktdetails

• Verlag: Oxford University Press, USA
• 2nd edition
• Seitenzahl: 270
• Erscheinungstermin: 18. November 1993
• Englisch
• Abmessung: 243mm x 164mm x 27mm
• Gewicht: 514g
• ISBN-13: 9780198537861
• ISBN-10: 0198537867
• Artikelnr.: 21862206

Inhaltsangabe

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