A unified syntactical approach to theorems of Putcha, Margolis, and Straubing on finite power semigroups
Short direct proofs are given of various results on (finite) power semigroups based on pseudoidentity manipulation. For instance, the pseudovariety generated by all power semigroups, the regular \({\mathcal J}\)- classes of which are aperiodic subsemigroups, is contained in a particular pseudovariety \(CJ\) (Straubing), the power semigroups of a pseudovariety \(V\) generate the pseudovariety of all semigroups if and only \(V\) contains the five-element combinatorial Brandt semigroup (Margolis), and if a simple group \(G\) divides the power semigroup of a finite semigroup \(S\), the regular \({\mathcal J}\)-classes of which form a subsemigroup, then \(G\) divides \(S\) (Putcha).
five-element combinatorial Brandt semigroup
scientific article; zbMATH DE number 150436
scientific article