Nilpotent subsemigroups on the semigroup of order-decreasing transformations
A. O. Stronska · Matematychni Studii · 2004
We consider the semigroup D n of order-decreasing transformations, i.e. transformations α of the set {1, ..., n}, such that xα x for any x in {1, ..., n}.We describe all the subsemigroups of D n which are maximal among the nilpotent subsemigroups of D n with nilpotency class k, prove that all these semigroups are pairwise nonisomorphic and derive formulas for calculation of number of such semigroups for nilpotency class 3 and 4.