Paper “On the p-length of some finite p-soluble groups” to appear in Israel J. of Math.

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A. Ballester-Bolinches, R. Esteban-Romero, L. M. Ezquerro

On the p-lenght of some finite p-soluble groups

Israel J. Math., in press

http://dx.doi.org/10.1007/s11856-014-1095-y

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Abstract:
The main aim of this paper is to give structural information of a finite group of minimal order belonging to a subgroup-closed class of finite groups and whose p-length is greater than 1, p a prime number. Alternative proofs and improvements of recent results about the influence of minimal p-subgroups on the p-nilpotence and p-length of a finite group
arise as consequences of our study.

 

http://permut.blogs.uv.es/?p=357

Paper “Primitive subgroups and PST-groups” published in Bull. Aust. Math. Soc

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

Primitive groups and PST-groups

Bull. Aust. Math. Soc., 89 (2014), 373–378

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

 

http://permut.blogs.uv.es/?p=353

Paper “Some subgroup embeddings in finite groups” accepted for publication 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

J. Adv. Res., in press

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

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

2010 Mathematics subject classification:

20D05, 20D10, 20F16

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

http://permut.blogs.uv.es/2014/05/01/paper-accepted-for-publication-in-j-adv-res/

International Conference “Classes of Groups, Algebras and their Applications” dedicated to the memory of Leonid A. Shemetkov, Gomel, Belarus, 3-6 July, 2014

L. A. ShemetkovOs traslado el anuncio de este congreso en Gomel, Bielorrusia:

The International Algebraic Conference “Classes of Groups, Algebras and their Applications”, dedicated to the memory of Corresponding Member of the National Academy of Sciences of Belarus, Honoured Scientist of Belarus, Doctor of Physical and Mathematical Sciences, Professor Leonid Alexandrovich Shemetkov will be held in Gomel on July 3-6, 2014.

http://agss-conf.org/shemetkov/

Deputy Chairman of the Organizing Committee M.V. Sel’kin

Program Committee Chairman A.N. Skiba

Executive Secretary V.A. Kovaleva

 

Adolfo Ballester-Bolinches and Ramón Esteban-Romero belong to the programme committee.

 

See also: http://permut.blogs.uv.es/2014/03/03/international-conference-classes-of-groups-algebras-and-their-applications-dedicated-to-the-memory-of-leonid-a-shemetkov-gomel-belarus-3-6-july-2014/

Paper “Algorithms for permutability in finite groups”

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

Algorithms for permutability in finite groups

Cent. Eur. J. Math., 11 (11), 1914-1922 (2013).

Abstract: In this paper we describe some algorithms to identify permutable and Sylow-permutable subgroups of finite groups, Dedekind and Iwasawa finite groups, and finite T-groups (groups in which normality is transitive), PT-groups (groups in which permutability is transitive), and PST-groups (groups in which Sylow permutability is transitive). These algorithms have been implemented in a package for the computer algebra system GAP.

Keywords:  Finite group • Permutable subgroup • S-permutable subgroup • Dedekind group • Iwasawa group • T-group • PT-group • PST-group • Algorithm
Mathematics Subject Classification (2010):  20D10, 20D20, 20-04

http://permut.blogs.uv.es/2013/08/14/paper-algorithms-for-permutability-in-finite-groups/

 

Paper “Primitive subgroups and PST-groups” to appear in Bull. Aust. Math. Soc.

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

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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

http://permut.blogs.uv.es/2013/07/25/paper-primitive-groups-and-pst-groups-to-appear-in-bull-aust-math-soc/

Paper “Graphs and classes of finite groups” published in Note Mat.

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A. Ballester-Bolinches, John Cossey, R. Esteban-Romero

Graphs and classes of finite groups

Note Mat., 33 (1), 89-94 (2013)

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

Abstract. There are different ways to associate to a finite group a certain graph. An interesting question is to analyse the relations between the structure of the group, given in group-theoretical terms, and the structure of the graph, given in the language of graph theory. This survey paper presents some contributions to this research line.
Keywords: finite groups, classes of groups, graphs
MSC 2000 classification: primary 20D10, secondary 05C25

http://permut.blogs.uv.es/2013/06/17/paper-graphs-and-classes-of-finite-groups-published-in-note-mat/