The rank of equivalence-preserving transformation semigroup T_E(X)
Lunzhi Deng · Journal of Guizhou Normal University · 2007
Let TX be the full transformation semigroup on the set X,for a nontrivial equivalence E on X,let TE(X)={f∈TX∶(a,b)∈E■(af,bf)∈E},then TE(X) is a subsemigroup of TX,it is called equivalence-preserving transformation semigroup.In this paper,we consider the rank of TE(X) for a special case that the set X is finite and the equivalence E has two classes,each of them has r,l(lr1) points.We first discuss the rank of the homemomorhism group G,then consider the rank of TE(X).It is found that TE(X) has a generating set containing Crl+7 elements,then we determine the rank of TE(X) is no more than Crl+7.