The Burnside Problem on Periodic Groups, and Related Problems

In a 1959–1975 cycle of papers, P.S. Novikov and S.I. Adian created a new method for studying periodic groups based on the classification of periodic words by means of a complicated simultaneous induction. The method was developed for solving the well-known Burnside problem on periodic groups, but it also enabled the authors to solve a number of other difficult problems of group theory. An extended survey of results contained in the cycle of papers mentioned above and of other significant results obtained after 1975 by Adian and other authors on the basis of the developed theory and its modifications is presented.