Power Semigroups of a Class of Clifford Semigroups

Abstract:

      Let $S=\bigcup (G_{\alpha}: \alpha\in E)$ be a semilattice of groups (i.e., a Clifford semigroup) and $n$ a natural number. $E$ is called an $n$-element chain of groups if it is an $n$-element chain. Denote by $\mathcal{C}_{n}$ the set of all $n$-element chains of groups. In this paper we shall show that for any natural number $n$, the class of semigroups $\mathcal{C}_{n}$ satisfies the strong isomorphism property.