On Burnside's problem on periodic groups
Burnside's problem, as is well known, consists in the following: Is every periodic group locally finite? Up to the present this question has been answered in the negative. The relevant examples were constructed first by E. S. Golod (1964) and P. S. Novikov and S. I. Adyan (1968). Later, other examples were constructed, notably Ol'shanskij's (1978), by means of which other important problems of the theory of periodic groups, namely, O. J. Schmidt's problem and that of S. N. Chernikov on groups with minimal condition, were also solved. The author gives a new, simply constructed example of a periodic group that is not locally finite. Specifically, the author constructs an infinite 2-group \(G\), generated by three involutions (i.e., elements of order 2) \(a\), \(b\) and \(c\), where \(b\) and \(c\) commute. Soon after the appearance of this paper it was established that the author's group \(G\) contains elements of arbitrarily high order (i.e., its exponential curve is not bounded) [see \textit{A. G. Ivanov} and \textit{A. V. Feklichev}, ``Unboundedness of the exponential curve of Grigorchuk's group'', Seventh All-Union Symposium on Group Theory (Shushenskoe, 1980) (Russian), Krasnoyarsk Gos. Univ., Krasnoyarsk, 1980].
scientific article; zbMATH DE number 3957421