Minimal congruences on finite transformation semigroups of weak Y-stabilizer
Xiuliang Yang · Journal of Zhejiang University(Science Edition) · 2011
Let T(X) be the full transformation semigroup on the finite set X,and Y a nonempty subset of X.Let W(Y)={α∈T(X)∶Yα■Y}.Prove that W(Y) exactly has two minimal congruences when 1|Y||X|;when |Y|=|X| or 1=|Y||X|,W(Y) has only one minimal congruence.