Some pseudovariety joins involving the pseudovariety of finite groups
Let ZE, IE, G, Com, and N denote respectively the pseudovarieties of (all finite) semigroups in which idempotents are central, semigroups which are nilpotent extensions of groups, groups, commutative semigroups, and nilpotent semigroups. It is shown that \(G\vee Com=ZE\) and \(G\vee (Com\cap N)=IE\), and a sublattice of the lattice of all pseudovarieties of semigroups containing all the above pseudovarieties is completely described. This settles some decidability conjectures proposed by Rhodes. The basic tools in the proofs are Reiterman's characterization of pseudovarieties in terms of pseudoidentities and the semigroup of n-ary implicit operations on ZE, whose structure was described by the author and Azevedo.
lattice of pseudovarieties of semigroups
scientific article; zbMATH DE number 4029841
scientific article