Stronska G. Structure of the subsemigroups of the order-decreasing transformations' semigroup.

The structure of maximal nilpotent subsemigroups of a given nilpotency degree for the semigroup of order-decreasing transformations of an arbitrary poset with zero is described. Maximal nilpotent subsemigroups of the semigroup of order-decreasing transformations of a chain are classified to isomorphism. Groups of automorphisms of maximal nilpotent subsemigroups of the semigroup of order-decreasing transformations of a chain are described. Criteria for two maximal nilpotent subsemigroups to be isomorphic are derived for the semigroup of order-decreasing transformations of an arbitrary poset with zero and the semigroup of order-decreasing transformations of the power set of a finite set.