On the rank of a kind of transformation semigroups
Pei Huisheng · 2004
Let TX be the full transformation semigroup on the set X, E be an equivalence on X, letTE(X)={f∈TX:(x,y)∈E,(f(x),f(y))∈E}.Then TE(X) is a subsemigroup of TX.In this paper,a special case is considered,that is,the equivalence E has two classes each of which is of n points.It is found that TE(X) has a generating set containing 5 elements.Then it is determined that the rank of TE(X) is no more than 5.