Abstract. A semigroup $S$ is called a permutable semigroup if $\alpha\circ \beta =\beta\circ \alpha $ is satisfied for all congruences $\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.

AMS Subject Classification (1991): 20M10

Keyword(s): permutable semigroups, Putcha semigroups, archimedean semigroups

Received April 28, 2009, and in revised form May 14, 2009. (Registered under 63/2009.)