Nilpotent subsemigroups of a semigroup of order-decreasing transformations of a rooted tree

Abstract

This paper deals with a semigroup of orderdecreasing transformations of a rooted tree. Such are the transformations α of some rooted tree G satisfying following condition: for any x from G α(x) belongs to a simple path from x to the root vertex of G. We describe all subsemigroups of the mentioned semigroup, which are maximal among nilpotent subsemigroups of nilpotency class k in our semigroup. In the event when rooted tree is a ray we prove that all these maximal subsemigroups are pairwise nonisomorphic.