Burnside groups

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, 2 J 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 ForschungsgemeinschafL, 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 splendid job in typing the notes. My personal thanks go to all the cooperators for their patience and efficiency. All the incompleteness of the present volume is my responsibility.