Paper “On partial CAP-subgroups of finite groups” published in J. Algebra

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

On partial CAP-subgroups of finite groups

J. Algebra, 431 (2015), 196–208

http://dx.doi.org/10.1016/j.jalgebra.2015.01.035

Abstract

Given a chief factor H/K of a finite group G, we say that a subgroup A of G avoids H/K if H∩A=K∩A; if HA=KA, then we say that A covers H/K. If A either covers or avoids the chief factors of some given chief series of G, we say that A is a partial CAP-subgroup of G. Assume that G has a Sylow p-subgroup of order exceeding pk. If every subgroup of order pk, where k≥1, and every subgroup of order 4 (when pk=2 and the Sylow 2-subgroups are non-abelian) are partial CAP-subgroups of G, then G is p-soluble of p-length at most 1.

2010 Mathematics subject classification: 20D10; 20D20

Keywords: Finite group; Partial CAP-subgroup; p-soluble group; p-length

 

Paper “A note on solubly saturated formations of finite groups” published in J. Algebra Appl.

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A. Ballester-Bolinches, S. F. Kamornikov

A note on solubly saturated formations of finite groups

J. Algebra Appl., 14(4) (2015), 1550047, 4

http://dx.doi.org/10.1142/S0219498815500474

Abstract

The main aim of this note is to give a criterion for a subgroup-closed formation to be solubly saturated, which we hope may provide a useful proving ground for outstanding questions about this family of formations.

Read More: http://www.worldscientific.com/doi/10.1142/S0219498815500474

2010 Mathematics subject classification20D10, 20D20

KeywordsFinite group; formation; saturation; soluble saturation

Paper “Some subgroup embeddings in finite groups: A mini-review” published in J. Adv. Res.

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A. Ballester-Bolinches, J. C. Beidleman, R. Esteban-Romero, M. F. Ragland

Some subgroup embeddings in finite groups: A mini-review

J. Adv. Res., 6(3) (2015), 359–362

http://dx.doi.org/10.1016/j.jare.2014.04.004

Abstract

In this survey paper several subgroup embedding properties related to some types of permutability are introduced and studied.

Keywords and phrases: Finite group; Permutability; S-permutability; Semipermutability; Primitive subgroup; Quasipermutable subgroup

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

First announcement Naples 2015 Conference in Group Theory and its applications

Oct ’15Oct
78

Dear Colleagues,
this is the first announcement of the Conference

Naples 2015 Conference in Group Theory and its applications

which will take place in Naples from Wednesday, October 7 to Thursday, October 8, 2015.

Invited speakers are:

  • Bernard Amberg (Mainz, Germany)
  • Adolfo Ballester-Bolinches (València , Spain)
  • Carlo Casolo (Firenze, Italy)
  • Dikran Dikranjan (Udine, Italy)
  • Alberto Facchini  (Padova, Italy)
  • Marco Fontana (Roma, Italy)
  • Antonino Giambruno (Palermo, Italy)
  • Patrizia Longobardi (Salerno, Italy)
  • Mercede Maj  (Salerno, Italy)
  • Derek J.S. Robinson (Urbana, USA)
  • Yaroslav P. Sysak (Kiev, Ukraine)

For more detailed information you can visit our web site in building

http://www.cgt2015.unina.it

In any case, for any question you can contact the organizers to the following e-mail address:

infocgt2015@unina.it

Please forward this announcement in your group and to people you think interested.

Thank you for cooperation.

Best wishes,

The organizers:
Francesco Catino
Maria De Falco
Maddalena Miccoli
Carmen Musella

Paper “On p-nilpotency of hyperfinite groups” published in Monatsh. Math.

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

On p-nilpotency of hyperfinite groups

Monatsh. Math., 176(4) (2015), 497–502

http://dx.doi.org/10.1007/s00605-014-0633-3

Abstract

Let p be a prime. We say that class X of hyperfinite p-groups determines p-nilpotency locally if every finite group G with a Sylow p-subgroup P in X is p-nilpotent if and only if N_G(P) is p-nilpotent. The results of this paper improve a recent result of Kurdachenko and Otal and show that if a hyperfinite group G has a pronormal Sylow p-subgroup in X, then G is p-nilpotent if and only if N_G(P) is p-nilpotent provided that X is closed under taking subgroups and epimorphic images. If X is not closed under taking epimorphic images, we have to impose local p-solubility to G. In this case, the hypothesis of pronormality can be removed.

2010 Mathematics subject classification: 20E15, 20F19, 20F22

Keywords: locally finite group; hyperfinite group; p-nilpotency

Paper “On fixed points of the lower set operator” published in Internat. J. Algebra Comput.

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J. Almeida, A. Cano, O. Klíma, J.-É. Pin

On fixed points of the lower set operator

Internat. J. Algebra Comput., 25(1-2) (2015), 259–292

http://dx.doi.org/10.1142/S021819671540010X

Abstract

Lower subsets of an ordered semigroup form in a natural way an ordered semigroup. This lower set operator gives an analogue of the power operator already studied in semigroup theory. We present a complete description of the lower set operator applied to varieties of ordered semigroups. We also obtain large families of fixed points for this operator applied to pseudovarieties of ordered semigroups, including all examples found in the literature. This is achieved by constructing six types of inequalities that are preserved by the lower set operator. These types of inequalities are shown to be independent in a certain sense. Several applications are also presented, including the preservation of the period for a pseudovariety of ordered semigroups whose image under the lower set operator is proper.Read More: http://www.worldscientific.com/doi/10.1142/S021819671540010X

2010 Mathematics subject classificationPrimary: 20M07, Secondary: 20M35

Keywords: Ordered semigroups; pseudovarieties; lower sets; power operator; inequalities; pseudoidentities

Visita de Paz Jiménez Seral

Abr ’15
15
15:00

Paz Jiménez

La profesora Paz Jiménez Seral, del Departamento de Matemáticas de la Universidad de Zaragoza, visita la Universitat de València entre el miércoles 15 y el viernes 17 de abril de 2015. Paz es investigadora del proyecto «Propiedades aritméticas y estructurales de los grupos, aplicaciones II», coordinado con el nuestro, y trabaja en el estudio de los grupos finitos a través de sus acciones y en clases de grupos finitos.

Paper “On a class of generalised Schmidt groups” published in Ann. Mat. Pura Appl.

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A. Ballester-Bolinches, R. Esteban-Romero, Qinhui Jiang, and Xianhua Li

On a class of generalised Schmidt groups

Ann. Mat. Pura Appl. (4), 194(1) (2015), 77–86

http://dx.doi.org/10.1007/s10231-013-0365-3

Abstract

In this paper families of non-nilpotent subgroups covering the non-nilpotent part of a finite group are considered. An A_5-free group possessing one of these families is soluble, and soluble groups with this property have Fitting length at most three. A bound on the number of primes dividing the order of the group is also obtained.

2010 Mathematics subject classification: 20D05; 20D10; 20F16

Keywords: finite groups; nilpotent groups; maximal subgroups