Although varieties of groups can in theory be determined as well by the identical relations which the groups all satisfy as by some structural property inherited by subgroups, factor groups and cartesian products which the groups have in common, it seems in practice just as hard to answer questions about properties of a group from knowledge of identical relations as it is from, say, a presentation. Many of the important questions connected with Burnside's problems exemplify this difficulty: we still do not know if there is a bound on the derived length of finite groups of exponent 4, nor whether there is a bound on the nilpotency class of finite groups of exponent p (p ≧ 5, a fixed prime).