Finite Permutable Putcha Semigroups

A semigroup $S$ is called a permutable semigroup if $\alpha \circ \beta =\beta \circ \alpha$issatifiedforallcongruences$\alpha$and$\beta$of$S$. A semigroup is called a Putcha semigroup if it is a semilattice of archimedean semigroups. In this paper we deal with finite permutable Putcha semigroups. We describe the finite permutable archimedean semigroups and finite permutable semigroups which are semilattices of a group and a nilpotent semigroup.