A note on the power semigroup of a completely simple semigroup. (Q927284)

Problem 54 of \textit{J. Almeida} [Finite semigroups and universal algebra. Series in Algebra 3. Singapore: World Scientific (1994; Zbl 0844.20039)] is solved. If \(\mathbf V\) is a pseudovariety, then \(\mathbf{PV}\) denotes the pseudovariety generated by power semigroups of members of \(\mathbf V\). Let \(\mathbf{CS}\) be the pseudovariety of completely simple semigroups, \(\mathbf{BG}\) the pseudovariety of block groups and \(\mathbf{RZ}\) the pseudovariety of right zero semigroups. The main result says that \(\mathbf{PCS}\) is the semidirect product of \(\mathbf{BG}\) with \(\mathbf{RZ}\). Because of this result, two open questions are proposed.