Some questions in the theory of varieties of groups

In this paper a new method of studying identity relations in groups is described. Among the results obtained by this method is an example of a group variety that does not have an independent basis of identities. A conjecture by P. Hall on marginal subgroups is refuted. The question of the relation between the representation of a group variety in the form of a union and the product of two proper subvarieties is considered. An example of a group variety having a set of continuum many different covering varieties is constructed and a number of results are obtained, as corollaries, on whether (solvable) group varieties can be generated by certain classes of groups.
Bibliography: 26 titles.