Archivo por meses: julio 2013

Paper «Extension of Schur theorem to groups with a central factor with a bounded section rank» published in J. Algebra

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The following paper has been published:

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A. Ballester-Bolinches, S. Camp-Mora, L. A. Kurdachenko, J. Otal

Extension of Schur theorem to groups with a central factor with a bounded section rank

J. Algebra, 393, 1-15 (2013)

http://dx.doi.org/10.1016/j.jalgebra.2013.06.035

Abstract: A well-known result reported by Schur states that the derived subgroup of a group is finite provided its central factor is finite. Here we show that if the p-section rank of the central factor of a locally generalized radical group is bounded, then so is the p-section rank of its derived subgroup. We also give an explicit expression for this bound.

MSC: 20F14, 20F19, 20F99

Keywords: Schur class, Schur multiplier, Special rank of a group, p-section rank of a group, 0-rank of a group, Generalized radical group

Paper «Primitive subgroups and PST-groups» to appear in Bull. Aust. Math. Soc.

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The following paper has been accepted for publication. We will inform about the publication details.

El siguiente artículo ha sido aceptado para su publicación. Informaremos sobre los detalles bibliográficos.

El següent article ha sigut acceptat per a la seua publicació. N’informarem sobre els detalls bibliogràfics.

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

Primitive groups and PST-groups

Bull. Aust. Math. Soc.

http://dx.doi.org/10.1017/S0004972713000592

Abstract

All groups considered in this paper are finite. A subgroup H of a group G is called a primitive subgroup if it is a proper subgroup in the intersection of all subgroups of G containing H as a proper subgroup. He et al. [‘A note on primitive subgroups of finite groups’, Commun. Korean Math. Soc. 28(1) (2013), 55–62] proved that every primitive subgroup of G has index a power of a prime if and only if G/Φ(G) is a solvable PST-group. Let X denote the class of groups G all of whose primitive subgroups have prime power index. It is established here that a group G is a solvable PST-group if and only if every subgroup of G is an X-group.

2010 Mathematics subject classification: primary 20D10; secondary 20D15, 20D20

Keywords and phrases: finite groups, primitive subgroups, solvable PST-groups, T0-groups

Paper «On a class of generalised Schmdit groups» published in Ann. Mat. Pura Appl.

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The paper

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

On a class of generalised Schmidt groups

will be published in Annali di Matematica Pura ed Applicata. It is available through

http://dx.doi.org/10.1007/s10231-013-0365-3
(see abstract below). We will inform about the publication details.

El artículo

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

On a class of generalised Schmidt groups

será publicado en Annali di Matematica Pura ed Applicata. Está disponible en

http://dx.doi.org/10.1007/s10231-013-0365-3
(véase resumen más abajo). Informaremos sobre los detalles de su publicación.

L’article

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

On a class of generalised Schmidt groups

serà publicat en Annali di Matematica Pura ed Applicata. Està disponible en

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

(vegeu resum més avall). Informarem sobre els detalls de la seua publicació.

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.

Keywords:  Finite groups · Nilpotent groups · Maximal subgroups
Mathematics Subject Classification (2010):  20D05 · 20D10 · 20F16

Paper «On generalised subnormal subgroups of finite groups» published in Math. Nachr.

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The paper

A. Ballester-Bolinches, James Beidleman, A. D. Feldman, M. F. Ragland,

On generalised subnormal subgroups of finite groups

has appeared in Mathematische Nachrichten, 286, No. 11-12, 1066-1171 (2013). It is available through

http://dx.doi.org/10.1002/mana.201200029

See abstract below.

 

El artículo

A. Ballester-Bolinches, James Beidleman, A. D. Feldman, M. F. Ragland,

On generalised subnormal subgroups of finite groups

ha aparecido en Mathematische Nachrichten, 286, No. 11-12, 1066-1171 (2013). Ya está accesible a través de

http://dx.doi.org/10.1002/mana.201200029

Véase el resumen al final.

 

L’article

A. Ballester-Bolinches, James Beidleman, A. D. Feldman, M. F. Ragland,

On generalised subnormal subgroups of finite groups

ha aparegut en Mathematische Nachrichten, 286, No. 11-12, 1066-1171 (2013). Està accessible per mitjà de

http://dx.doi.org/10.1002/mana.201200029

Al final se’n pot veure el resum.

 

Abstract:

Let F be a formation of finite groups. A subgroup M of a finite group G is said to be F-normal in G if G/CoreG(M) belongs to F. A subgroup U of a finite group G is called a K-F-subnormal subgroup of G if either U = G or there exist subgroups U = U0 ≤ U1 ≤ … ≤ Un = G such that Ui − 1 is either normal or F-normal in Ui, for i = 1, 2, …, n. The K-F-subnormality could be regarded as the natural extension of the subnormality to formation theory and plays an important role in the structural study of finite groups. The main purpose of this paper is to analyse classes of finite groups whose K-F-subnormal subgroups are exactly the subnormal ones. Some interesting extensions of well-known classes of groups emerge.

Keywords: Formation; F-subnormal Subgroup; Subnormal Subgroup; PST-groups; PT-groups; T-groups

MSC (2010): 20D10; 20D35; 20F17

 

https://permut.blogs.uv.es/2013/04/02/paper-on-generalised-subnormal-subgroups-of-finite-groups/

Paper «Mutually permutable products and conjugacy classes» published in Monatsh. Math.

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The following paper has been published.

El siguiente artículo ha sido publicado.

El següent article ha sigut publicat.

A. Ballester-Bolinches, John Cossey, Yangming Li

Mutually permutable products and conjugacy classes

Monatsh. Math., 170, 305-310 (2013)

http://dx.doi.org/10.1285/i15900932v33n1p89

Abstract

A subgroup A of a finite group G is said to be S-permutably embedded in G if for each prime p dividing the order of A, every Sylow p-subgroup of A is a Sylow p-subgroup of some S-permutable subgroup of G. In this paper we determine how the S-permutable embedding of several families of subgroups of a finite group influences its structure

Keywords: Finite group, Permutability, S-permutability, Maximal subgroups,
Minimal subgroups

Mathematics Subject Classification (2010): 20D05, 20D10, 20D35, 20F17