Finite Permutable Putcha Semigroups

A semigroup $S$ is called a permutable semigroup if $α\circ β=β\circ α$ is satified for all congruences $α$ and $β$ 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.

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