Automorphisms of partition order-decreasing transformation monoids

摘要

Let T_n be the full transformation semigroup on a finite set X_n={1,2,...,n}. Let ρ be an equivalence relation on X_n and ≤ be a total order on the partition set X_n/ρ. We describe all automorphisms of the partition order-decreasing transformation monoid:, that generalizes the results of Schreier (Fundam. Math., 28:261-264, 1936) and ?utov (Izv. Vys?. U?ebn. Zaved., Mat., 3:177-184, 1961).