Quasivarieties of groups closed with respect to restricted wreath products

This paper studies quasivarieties of groups, closed under restricted wreath products. It is shown that if a class $\mathfrak R$ of groups is closed with respect to restricted wreath products, then the quasivariety generated by $\mathfrak R$ is also closed under restricted wreath products. The base rank of a nontrivial quasivariety, closed under restricted wreath products, is found to be two. Conditions are given that ensure that a countable group from a given quasivariety is isomorphically embeddable in a 2-generator group from the same quasivariety. Finally, the cardinality of the set of all quasivarieties that consist of torsionfree groups and are closed with respect to restricted wreath products is computed.
Bibliography: 12 titles.