On the relative solvability of certain inverse monoids

The notion of kernel of a finite monoid relative to a pseudovariety of groups can be used to define relative solvability of monoids in a similar way to the manner in which the notion of derived subgroup can be used to define solvable group. In this paper we study the solvability of certain inverse monoids relative to pseudovarieties of abelian groups.This work was partly supported by Fundação para a Ciência e a Tecnologia (FCT) through the Centro de Matemática da Universidade do Porto (CMUP) and by the project PTDC/MAT/65481/2006, which is partly funded by them European Community Fund FEDER. The second author gratefully acknowledges also the ESF programme “Au-tomata: from Mathematics to Applications (AutoMathA)” within whose framework the work leading to this paper has been carried out