Paper “Languages associated with saturated formations of groups” published in Forum Math.

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Adolfo Ballester-Bolinches, Jean-Éric Pin, Xaro Soler-Escrivà

Languages associated with saturated formations of groups

Forum Math., 27(3) (2015), 1471–1505

http://dx.doi.org/10.1515/forum-2012-0161

Abstract

In a previous paper, the authors have shown that Eilenberg’s variety theorem can be extended to more general structures, called formations. In this paper, we give a general method to describe the languages corresponding to saturated formations of groups, which are widely studied in group theory. We recover in this way a number of known results about the languages corresponding to the classes of nilpotent groups, soluble groups and supersoluble groups. Our method also applies to new examples, like the class of groups having a Sylow tower.

2010 Mathematics subject classification68Q70; 20D10

KeywordsGroup formation; regular language; finite automata; finite monoid

Paper “Languages associated with saturated formations of groups” to appear in Forum Math.

The paper

Adolfo Ballester-Bolinches, Jean-Éric Pin, Xaro Soler-Escrivà

Languages associated with saturated formations of groups

will be published in Forum Mathematicum. It is available through

http://dx.doi.org/10.1515/forum-2012-0161

We will inform about the publication details. See abstract below.

El artículo

Adolfo Ballester-Bolinches, Jean-Éric Pin, Xaro Soler-Escrivà

Languages associated with saturated formations of groups

será publicado en Forum Mathematicum. Está disponible en

http://dx.doi.org/10.1515/forum-2012-0161

Informaremos sobre los detalles de publicación. Véase el resumen más abajo.

 

L’article

Adolfo Ballester-Bolinches, Jean-Éric Pin, Xaro Soler-Escrivà

Languages associated with saturated formations of groups

serà publicat en Forum Mathematicum. Està disponible a

http://dx.doi.org/10.1515/forum-2012-0161

Informarem sobre els detalls de publicació. Vegeu el resum més avall.

 

Abstract

In a previous paper, the authors have shown that Eilenberg’s variety theorem can be extended to more general structures, called formations. In this paper, we give a general method to describe the languages corresponding to saturated formations of groups, which are widely studied in group theory. We recover in this way a number of known results about the languages corresponding to the classes of nilpotent groups, soluble groups and supersoluble groups. Our method also applies to new examples, like the class of groups having a Sylow tower.

Keywords: Group formation; regular language;finite automata; finite monoid