Burnside Groups Proceedings of a Workshop Held at the University of
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806 Burnside Groups
Proceedings of a Workshop Held at the University of Bielefeld, Germany June-July 1977
Edited by J. L. Mennicke
Springer-Verlag Berlin Heidelberg New York 1980
Editor Jens L. Mennicke Universit~t Bielefeld, 4800 Bielefeld, Federal Republic of Germany
Assisted by F. J. Grunewald Sonderforschungsbereich, Theoretische Mathematik Universit~t Bonn, 5300 Bonn, Federal Republic of Germany G. Havas, M. F. Newman Department of Mathematics, Institute of Advanced Studies Australian National University, Canberra, ACT 2600, Australia
AMS Subject Classifications (1980): 20-02, 20-04, 20E10, 20F05, 20F10, 20F50 ISBN 3-540-10006-7 Springer-Verlag Berlin Heidelberg NewYork ISBN 0-387-10006-7 Springer-Verlag NewYork Heidelberg Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin Heidelberg 1980 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
PREFACE
The present notes arose out of a workshop which was held at the University of Bielefeld in summer 1977. The main purpose of the workshop was to survey the present knowledge on Burnside groups, in particular the work of Novikov-Adian. The technical difficulties of this work are such that communication becomes a serious problem. The editors hope that the notes of Professor Adian's lectures will help a prospective reader to find access to the work which is now available in book form. The original Russian book was translated into English by Wiegold and Lennox and has appeared in the Ergebnisse series.
A first attack on the finiteness problem for B(2, 8) is a second part of these notes. The authors are well aware of the incompleteness of the present results. They hope, however, that some of the methods and techniques may be helpful for future progress. The workers in the field seem to agree that the structure of B[2, 2k] should become stable for some k . However, it is not even clear whether one should expect that for large k these groups are finite or infinite. It seems clear, however, that B(2, 8) should be an important test case. M.F. Newman has compiled a list of problems which we hope will stimulate interest. It is a pleasure to acknowledge financial support from Deutsche Forschungsgemeinschaft, Heinrich-Hertz-Stiftung, and University of Bielefeld. Our thanks go to the participants, in particular to Professor Sergej I. Adian who did the bulk of the lecturing. Our thanks also go to the technical staff for their valuable help: to the secretaries of the Department of Mathematics, and to the staff of ZiF in Bielefeld, and in particular to Mrs B.M. Geary who did a
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