Visita de Jean-Éric Pin (08-15/10/2016)

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Jean-Éric PinEstimadas compañeras, estimados compañeros:

El profesor Jean-Éric Pin, del Institut de Recherche en Informatique Fondamentale (IRIF), CNRS y Université Paris-Diderot, visitará el Departament de Matemàtiques entre el 8 y el 15 de octubre. El profesor Pin es especialista en la teorías de semigrupos y de autómatas y lenguajes formales. Durante su visita impartirá un curso de seis horas titulado

«Stone duality and formal languges»

los días

  • martes 11, 15.00-17.00,
  • jueves 13, 12.00-14.00,
  • viernes 14, 11.00-13.00

en el seminario de Álgebra del segundo piso de la Facultat de Matemàtiques.

Quedáis todos invitados.

Cordialmente,

Ramón

Paper “On finite p-nilpotent groups” published in Monatsh. Math.

The following paper has been published

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El següent article ha sigut publicat

Adolfo Ballester-Bolinches, Xiuyun Guo, Yangming Li, and Ning Su.

On finite p-nilpotent groups.

Monatsh. Math., 181(1):63–70, 2016

https://doi.org/10.1007/s00605-015-0803-y

Abstract

In this paper the structure of a minimal counterexample among the non-p-nilpotent groups having p-nilpotent p-Sylow normalisers is analysed. Several p-nilpotency criteria and many earlier results follow from our main theorem.

2010 Mathematics Subject Classification: 20D10, 20D20

Keywords: Finite groups, p-nilpotency, Minimal subgroups, Sylow normalisers

Paper “On bounds for the p-length of finite p-soluble groups” published in Collect. Math.

The following paper has been published

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Adolfo Ballester-Bolinches, Luis M. Ezquerro, and Ning Su.

On bounds for the p-length of finite p-soluble groups.

Collect. Math., 67(3):373–378, 2016.

https://doi.org/10.1007/s13348-015-0144-0

Abstract

The aim of this paper is to obtain a bound for the p-length of a p-soluble group G whose elements of order p or order 4 (if p=2) of a Sylow p-subgroup of a residual subgroup of G are contained in the k-th term of the upper central series of a Sylow p-subgroup of G.

2010 Mathematics Subject Classification: 20D10, 20D20

Keywords: Finite group, p-soluble group, p-length

Visita del profesor Jorge Almeida (31/08-07/09/2016)

Ago ’16Sep
317

Estimados compañeros, estimadas compañeras:

El profesor Jorge Almeida (Universidade do Porto, Portugal) visitará el Departament de Matemàtiques entre el 31 de agosto y el 7 de septiembre de 2016. Es experto en teoría de semigrupos, autómatas y lenguajes formales. Durante su estancia impartirá dos charlas:

  • Viernes 2 de septiembre, 12.00 h
    Seminario del Instituto Universitario de Matemática Pura y Aplicada
    Universitat Politècnica de València
    «Recent progress on concatenation hierarchies of star-free languages»
    Resumen:
    A celebrated theorem of Schützenberger (1965) states that a language can be expressed in the letters using only finite union, complementation, and concatenation (the so-called star-free languages) if and only if its syntactic semigroup has only trivial subgroups. On the other hand, McNaughton and Papert (1971) showed that such languages are precisely those that may be defined by first order sentences, where words are viewed as finite linear orders with predicates for each letter to express that the letter appears in a specific position. The combination of the two theorems provides an algorithm to decide when a regular language admits such a definition. A further ingredient was given by W. Thomas (1982), who showed that the analogue of the arithmetical hierarchy in this context, determined by the alternation of quantifiers, is intimately connected with the alternation of the closures under union, intersection, and concatenation, versus union and complementation, a hierarchy first introduced by Brzozowski (1971). The major open problem in this area is whether one can compute the minimum number of quantifier alternations needed to define a given star-free language. The purpose of the talk is to survey recent progress on this topic.
  • Martes 6 de septiembre, 12.00 h
    Seminario de Álgebra, Departament de Matemàtiques
    Universitat de València
    «Rauzy graphs and the free profinite semigroup»
    Resumen:
    Symbolic dynamical systems have been studied from many viewpoints, in particular in an attempt to classify them. Several algebraic and combinatorial structures have been associated to them. In the case of minimal systems, we have established a relationship between Rauzy graphs, which describe the successive reading of blocks of symbols of fixed length and certain profinite subgroups of the free profinite semigroup on the underlying set of symbols. More precisely, we have shown that these groups may be obtained as inverse limits of the profinite completions of the fundamental groups of the Rauzy graphs as the length of the blocks varies. This is joint work with Alfredo Costa (University of Coimbra).

Cordialmente,

Ramón.

 

Paper “Group extensions and graphs” published in Expo. Math.

The following paper has been published

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A. Ballester-Bolinches, E. Cosme-Llópez, and R. Esteban-Romero.

Group extensions and graphs.

Expo. Math., 34(3):327–334, 2016

https://doi.org/10.1016/j.exmath.2015.07.005

Abstract

A classical result of Gaschütz affirms that given a finite A-generated group G and a prime p , there exists a group G^# and an epimorphism φ:G→G^# whose kernel is an elementary abelian p-group which is universal among all groups satisfying this property. This Gaschütz universal extension has also been described in the mathematical literature with the help of the Cayley graph. We give an elementary and self-contained proof of the fact that this description corresponds to the Gaschütz universal extension. Our proof depends on another elementary proof of the Nielsen–Schreier theorem, which states that a subgroup of a free group is free.

2010 Mathematical Subject Classification: Primary 20F65; Secondary 05C25, 20D20, 20E22, 20F05, 20F10

Keywords: Group, Group extension, Graph

Paper “On groups whose subgroups of infinite rank are Sylow permutable” published in Ann. Mat. Pura Appl.

The following paper has been published

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A. Ballester-Bolinches, S. Camp-Mora, L. A. Kurdachenko, and F. Spagnuolo.

On groups whose subgroups of infinite rank are Sylow permutable.

Ann. Mat. Pura Appl. (4), 195(3):717–723, 2016.

https://doi.org/10.1007/s10231-015-0485-z

Abstract

In this paper, we investigate the structure of locally finite groups of infinite section rank (respectively, special rank) whose subgroups of infinite section rank (respectively, special rank) are Sylow permutable, permutable or normal. Some earlier results for locally finite groups appear as consequences of our study.

2010 Mathematics Subject Classification: 20E15, 20F19, 20F22

Keywords: Locally finite group, Section p-rank, Section rank, Special rank, Permutable, Sylow permutable, Normal

Paper “Triple Factorizations and Supersolubility of Finite Groups” published on Proc. Edinb. Math. Soc.

The following paper has been published

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Adolfo Ballester-Bolinches and Luis M. Ezquerro.

Triple factorizations and supersolubility of finite groups.

Proc. Edinb. Math. Soc. (2), 59(2):301–309, 2016.

https://doi.org/10.1017/S0013091515000231

Abstract

In this paper we analyse the structure of a finite group of minimal order among the finite non-supersoluble groups possessing a triple factorization by supersoluble subgroups of pairwise relatively prime indices. As an application we obtain some sufficient conditions for a triple factorized group by supersoluble subgroups of pairwise relatively prime indices to be supersoluble. Many results appear as consequences of our analysis.

Keywords: Finite group, Supersoluble group, Factorization

Paper “On generalised FC-groups in which normality is a transitive relation” published in J. Aust. Math. Soc.

The following paper has been published

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R. Esteban-Romero and G. Vincenzi.

On generalised FC-groups in which normality is a transitive relation.

 J. Aust. Math. Soc., 100(2):192–198, 2016

https://doi.org/10.1017/S1446788715000397

Abstract

We extend to soluble FC-groups, the class of generalised FC-groups introduced in de Giovanni et al. [‘Groups with restricted conjugacy classes’, Serdica Math. J. 28(3) (2002), 241–254], the characterisation of finite soluble T-groups obtained recently in Kaplan [‘On T-groups, supersolvable groups, and maximal subgroups’, Arch. Math. (Basel) 96(1) (2011), 19–25].

2010 Mathematical Subject Classification: Primary 20F24; Secondary 20E34, 20F14, 20F19

Paper “A note on a result of Guo and Isaacs about p-supersolubility of finite groups” published in Arch. Math. (Basel)

The following paper has been published

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Adolfo Ballester-Bolinches, Ramón Esteban-Romero, and ShouHong Qiao.

A note on a result of Guo and Isaacs about p-supersolubility of finite groups.

Arch. Math. (Basel), 106(6):501–506, 2016.

https://doi.org/10.1007/s00013-016-0901-7

Abstract

In this note, global information about a finite group is obtained by assuming that certain subgroups of some given order are S-semipermutable. Recall that a subgroup H of a finite group G is said to be S-semipermutable if H permutes with all Sylow subgroups of G of order coprime to |H|. We prove that for a fixed prime p, a given Sylow p-subgroup P of a finite group G, and a power d of p dividing |G| such that 1d<|P|, if HO^p(G) is S-semipermutable in O^p(G) for all normal subgroups H of P with |H|=d, then either G is p-supersoluble or else |PO^p(G)|>d. This extends the main result of Guo and Isaacs in (Arch. Math. 105:215–222 2015). We derive some theorems that extend some known results concerning S-semipermutable subgroups.

2010 Mathematical Subject Classification: 20D10, 20D20

Keywords: Finite group, p-supersoluble group, S-semipermutable subgroup

Paper “Z-permutable subgroups of finite groups” published in Monatsh. Math.

The following paper has been published

El siguiente artículo ha sido publicado

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A. A. Heliel, A. Ballester-Bolinches, R. Esteban-Romero, and M. O. Almestady.

Ζ-permutable subgroups of finite groups.

Monatsh. Math., 179(4):523–534, 2016

https://doi.org/10.1007/s00605-015-0756-1

Abstract

Let be a complete set of Sylow subgroups of a finite group G, that is, a set composed of a Sylow p-subgroup of G for each p dividing the order of G. A subgroup H of G is called -permutable if H permutes with all members of . The main goal of this paper is to study the embedding of the -permutable subgroups and the influence of -permutability on the group structure.

2010 Mathematics Subject Classification: 20D10, 20D20, 20D35, 20D40

Keywords: Finite group, p-soluble group, p-supersoluble, ℨ-permutable subgroup, Subnormal subgroup