Paper «On Sylow permutable subgroups of finite groups» published in Forum Math.

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Adolfo Ballester-Bolinches, Hermann Heineken and Francesca Spagnuolo.
On Sylow permutable subgroups of finite groups.
Forum Math., 29(6):1307-1310, 2017.

Abstract:

A subgroup H of a group G is called Sylow permutable, or S-permutable, in G if H permutes with all Sylow p-subgroups of G for all primes p. A group G is said to be a PST-group if Sylow permutability is a transitive relation in G. We show that a group G which is factorised by a normal subgroup and a subnormal PST-subgroup of odd order is supersoluble. As a consequence, the normal closure S^G of a subnormal PST-subgroup S of odd order of a group G is supersoluble, and the subgroup generated by subnormal PST-subgroups of G of odd order is supersoluble as well.

doi: 10.1515/forum-2016-0262

2020 Mathematics Subject Classification: 20D20, 20D35, 20D40, 20E15.

Keywords: Finite groups, subnormal subgroups, permutability, S-permutability.

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 «Formations of finite monoids and formal languages: Eilenberg’s variety theorem revisited» published in Forum Math.

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

Formations of finite monoids and formal languages: Eilenberg’s variety theorem revisited

Forum Math., 26(6) (2014), 1737–1761

http://dx.doi.org/10.1515/forum-2012-0055

Abstract

We present an extension of Eilenberg’s variety theorem, a well-known result connecting algebra to formal languages. We prove that there is a bijective correspondence between formations of finite monoids and certain classes of languages, the formations of languages. Our result permits to treat classes of finite monoids which are not necessarily closed under taking submonoids, contrary to the original theory. We also prove a similar result for ordered monoids.

2010 Mathematics subject classification: 20D10; 20M35

KeywordsGroup formations; regular languages; semigroups; automata theory

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