Abelian Kernels, Solvable Monoids and the Abelian Kernel Length of a Finite Monoid

Abstract

The notion of abelian kernel of a finite monoid extends the notion of derived subgroup of a finite group. Extensions to finite monoids of the notions of solvable group and derived length of a solvable group appear then naturally. In this paper we study these notions for some classes of finite monoids.

On the relative solvability of certain inverse monoids

“…We follow the notation introduced in [5]. The following result, which will allow us to give an upper bound for the length of the H π -kernel chain of some inverse monoids, is a generalization of [5, Proposition 2.1], proved by Fernandes and the second author.…”

“…The following result, which will allow us to give an upper bound for the length of the H π -kernel chain of some inverse monoids, is a generalization of [5, Proposition 2.1], proved by Fernandes and the second author. Its proof, consisting mostly of straightforward generalizations of results from [5], can be checked in [2]. Proposition 5.2.…”

“…The inverse monoids POI n , PODI n , POPI n , PORI n and I n . For a quick survey on these monoids, we suggest the paper [10] by Fernandes or any of the papers closely related to the present one: [5,1]. References for a deeper understanding of these monoids can be found there.…”

“…It is inspired in part of the paper [5] by Fernandes and the second author, where the question has been treated for the same monoids and the (non relative) abelian kernel.…”

Computing relative abelian kernels of finite monoids

“…This algorithm is presently part of a GAP package in preparation which will probably also contain implementations of the algorithms described in this paper. The usefulness of this software can be inferred from a number of papers whose original motivation came from computations done: we can refer to several joint works by Fernandes and the second author [5][6][7][8].…”