PSEUDOFINITE S-ACTS

The work has begun to study the structure of pseudofinite acts over a monoid. A theorem on the finiteness of an arbitrary cyclic subacts of S-act is proved under the condition that this S-act is pseudofinite and the number of types of isomorphisms of finite cyclic S-acts is finite. It is shown that a coproduct of finite S-acts is pseudofinite. As a consequence, it is shown that any S-act, where S is a finite group, is pseudofinite.