Kochubinska Y. Semigroups of partial automorphisms of rooted trees.

Semigroups of partial automorphisms of rooted trees are studied. Special attention is paid to subsemigroups of this semigroup, namely generalized bicyclic semigroup B (n) and semigroup ConPAutT of partial automorphism that preserve levels of vertices and domain of that is connected and contain root vertex. Basic semigroup theory problems are studied for them. Permutational representations on the set of right classes by closed inverse subsemigroups are constructed. Abstract characterization of semigroup ConPAutT is given. It is proved that semigroup ConPAutT is isomorphic to partial wreath power of inverse symmetric semigroup ISn. Properties of partial wreath power of ISn are studied.Combinatorial questions are studied. Cross-sections of Green's relations of partial wreath product of inverse symmetric semigroups are described and classified up to isomorphism.