<i>S_n</i>-normal semigroups

Abstract

Certain subsemigroups of the full transformation semigroup T n on a finite set of cardinality n are investigated, namely those subsemigroups S of T n , which are normalised by the symmetric group on n elements, the group of units of T n . The S n -normal closure of an element of T n is determined, and the structure of the S n -normal ideals consisting of the members of T n whose image contains at most r elements is studied.