Action-type axiomatizable classes of group representations

The paper adjoins the book of B. I. Plotkin and S. M. Vovsi Varieties of Representations of Groups (Zinatne, Riga (1983)) and turns to be, in a sense, its continuation. In the book, the varieties of representations have been considered. As a matter of fact, the varieties under consideration are action-type varieties. This paper studies other classes of representations, axiomatizable in a special action-type logic.