Shafranova G. Nilpotent subsemigroups of semigroups of transformations

Nilpotent subsemigroups of the inverse symmetric semigroup IS(М) and the semigroup PAutq(Vn) of all partial automorphisms of a finite vector space are considered in the dissertation. The structure of maximal nilpotent subsemigroups of a fixed nilpotence degree for the semigroups IS(M) and PAutq(Vn) is described and criteria of isomorphism of such subsemigroups are given. A simple description of the group of automorphisms of a maximal nilpotent subsemigroup T from IS(M) is obtained. The structure of lattices of ideals of maximal nilpotent subsemigroups of the finite inverse symmetric semigroup IS(M) is investigated.