Computing relative abelian kernels of finite monoids

Let H be a pseudovariety of abelian groups corresponding to a recursive supernatural number. In this note we explain how a concrete implementation of an algorithm to compute the kernel of a finite monoid relative to H can be achieved. The case of the pseudovariety Ab of all finite abelian groups was already treated by the second author and plays an important role here, where we will be interested in the proper subpseudovarieties of Ab. Our work relies on an algorithm obtained by Steinberg

Solvable monoids with commuting idempotents

International Journal of Algebra and Computation, 15, nº 3 (2005), p. 547-570The notion of Abelian kernel of a nite monoid extends the notion of derived subgroup of a nite group. In this line, an extension of the notion of solvable group to monoids is quite natural: they are the monoids such that the chain of Abelian kernels ends with the submonoid generated by the idempotents. We prove in this paper that the nite idempotent commuting monoids satisfying this property are precisely those whose subgroups are solvable

Relative abelian kernels of some classes of transformation monoids

We consider members of some well studied classes of finite transformation monoids and give descriptions of their abelian kernels relative to decidable pseudovarieties of abelian groups

Commutative Images Of Rational Languages And The Abelian Kernel Of A Monoid

Natural algorithms to compute rational expressions for recognizable languages, even those working well in practice, may produce very long expressions. So, aiming towards the computation of the commutative image of a recognizable language, one should avoid passing through an expression produced this way. We modify here one of those algorithms in order to compute directly a semilinear expression for the commutative image of a recognizable language. We also give a second modication of the algorithm which allows the direct computation of the closure in the pronite topology of the commutative image. As an application, we give a modication of an algorithm for computing the Abelian kernel of a finite monoid obtained by the author in 1998 which is much more efficient in practice