Sumaryuk M. Free semigroups and groups which are generated by functional transformations

Free semigroups and groups which are generated by the functions of the real or complex variable are investigated in dissertation work, with different functional properties. New sufficient conditions of analytical character are determined. Under their implementation the semigroup or group, generated by specific type of functional transformations will be free. In particular, the concrete images of free 2-generated semigroups by those or other functions and image of free group of countable rank by monotonous and elementary functions with real variable are built. Proved that set of free k-generated subsemigroups of metabelian group of integer linear transformations of the uncountable numeric fields is more than collection of it k-generated subsemigroups, which are not free. The free semigroups of analytical functions, which are laid out in the rows of degree of certain kind are studied.