Quasiidentities and direct wreaths of groups
The author continues his study of quasivarieties of groups, concentrating here on their connections with standard wreath products of groups, here called direct wreaths. For a given class of groups R, he defines qwr R to be the least quasivariety closed with respect to wreath products and containing R. The main results state that if G is a finite nontrivial group, a torsion-free group in a special class which includes cyclic groups and torsion free nilpotent groups or a group with one defining relator, then qwr G cannot be defined by a system of quasiidentities stable with respect to wreath products. The set of such quasivarieties has the cardinal of the continuum.
scientific article; zbMATH DE number 3927195