The Burnside Groups and Small Cancellation Theory

In a pair of recent articles, the author develops a general version of small cancellation theory applicable in higher dimensions ([5]), and then applies this theory to the Burnside groups of sufficiently large exponent ([6]). More specifically, these articles prove that the free Burnside groups of exponent n ≥ 1260 are infinite groups which have a decidable word problem. The structure of the finite subgroups of the free Burnside groups is calculated from the automorphism groups of the general relators used in the presentation. The present article gives a brief introduction to the methods and techniques involved in the proof. Many of the ideas originate with the recent work of A. Yu. Ol’shanskii and S. V. Ivanov. Some familiarity with their work on the Burnside problem will be assumed.