Paper “Some contributions to the theory of transformation monoids” published in J. Algebra

The following paper has been published:

El siguiente artículo ha sido publicado:

El següent article ha sigut publicat:

A. Ballester-Bolinches, E. Cosme-Llópez, P. Jiménez-Seral.

Some contributions to the theory of transformation monoids

J. Algebra., 522:31-60, 2019

doi:10.1016/j.jalgebra.2018.12.005

Abstract

The aim of this paper is to present some contributions to the theory of finite transformation monoids. The dominating influence that permutation groups have on transformation monoids is used to describe and characterise transitive transformation monoids and primitive transitive transformation monoids. We develop a theory that not only includes the analogs of several important theorems of the classical theory of permutation groups but also contains substantial information about the algebraic structure of the transformation monoids. Open questions naturally arising from the substantial paper of Steinberg (2010) [11] have been answered. Our results can also be considered as a further development in the hunt for a solution of the Černý conjecture.

2010 Mathematics Subject Classification: 16W22, 20M30

Keywords: monoid theory, monoid action, transitive, faithful, primitive

Paper “A noncommutative extension of Mahler’s theorem on interpolation series” published in European J. Combin.

The following paper has been published.

El siguiente artículo ha sido publicado.

El següent article ha sigut publicat.

Jean-Éric Pin, Pedro V. Silva

A noncommutative extension of Mahler’s theorem on interpolation series

European J. Combin., 36, 564-578 (2014)

http://dx.doi.org/10.1016/j.ejc.2013.09.009

Abstract

In this paper, we prove an extension of Mahler’s theorem on interpolation series, a celebrated result of p-adic analysis. Mahler’s original result states that a function from N to Z is uniformly continuous for the p-adic metric dp if and only if it can be uniformly approximated by polynomial functions. We prove the same result for functions from a free monoid A∗ to Z, where dp is replaced by the pro-p metric, the profinite metric on A∗ defined by p-groups.