Engel groups. I
An \(n\)-Engel relator \(R\) is an \(n\)-times iterated commutator of an element \(A\) of the free group \({\mathcal F}\) by an element \(B\in{\mathcal F}\), that is to say, \(R=[A,nB]\), where \([A,0B]=A\), and \([A,nB]=[[A,(n-1)B],B]\). The paper under review is the first one of a series whose aim is a study of relatively free \(n\)-Engel groups through their presentations. It is devoted to the study of groups with a single Engel relator. Using diagrams, a description of all the consequences of this relator is given. The details are rather technical.
scientific article; zbMATH DE number 4163145