Articles liés à The Restricted Burnside Problem
Synopsis
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, in different guises, has inspired a considerable amount of research. This book aims to give a comprehensive account of a variant on the Burnside problem - the restricted Burnside problem. Making extensive use of Lie ring techniques it allows a uniform treatment of the field and includes Kostrikin's theorem for groups of prime exponent as well as detailed information on groups of small exponent. The treatment is intended to be self-contained and as such will be valuable to postgraduate students and research workers in the field. The author has included extensive details of the use of computer algebra to verify computations.
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Présentation de l'éditeur
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.
Revue de presse
Altogether the author has produced a thorough and nearly complete study of that important topic which additionally is garnished with a lot of new approaches. (Monafshefte fur Mathematik, 4 March 1995)
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
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The Restricted Burnside Problem (London Mathematical Society Monographs)
Edité par
Oxford University Press, 1990
ISBN 10 : 0198535732
ISBN 13 : 9780198535737
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