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

Charla de Guo Xiuyun

Feb ’14
10
11:00

GuoXiuyunEl profesor Guo Xiuyun, de la Universidad de Shanghai, impartirá la charla titulada

«The automizers and normalizers in finite groups»

el próximo lunes 10 de febrero de 2014, a las 11.00, en el seminario del Departament d’Àlgebra de la Universitat de València (2º piso de la Facultat de Matemàtiques).

Estáis todos invitados.

 

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.

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 conjugacy of supplements of normal subgroups of finite groups” to appear in Bull. Aust. Math. Soc.

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

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A. Ballester-Bolinches, Luis M. Ezquerro,

On conjugacy of supplements of normal subgroups of finite groups

Bull. Aust. Math. Soc.

http://dx.doi.org/10.1017/S0004972713000506

Abstract: The objective of this paper is to find some sufficient conditions to ensure the conjugacy of supplements of a normal subgroup of a soluble group.

2010 Mathematics subject classification: primary 20D10; secondary 20D20.
Keywords and phrases: finite groups, supplements, Schunck classes, formations.

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

The following paper has been published.

El siguiente artículo ha sido publicado.

El següent article ha sigut publicat.

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

Paper “On S-permutably embedded subgroups of finite groups” to appear in Monatsh. Math.

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A. Ballester-Bolinches,  Yangming Li

On S-permutably embedded subgroups of finite groups

Monatsh. Math.

http://dx.doi.org/10.1007/s00605-013-0497-y

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 groups, permutability, S-permutability, maximal subgroups, minimal subgroups
Mathematics Subject Classification: 20D05, 20D10, 20D35, 20F17

Paper “Mutually permutable products and conjugacy classes” to appear in Monatsh. Math.

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, John Cossey, Yangming Li

Mutually permutable products and conjugacy classes

Monatsh. Math.

http://dx.doi.org/10.1007/s00605-012-0411-z

Abstract: The question of how certain arithmetical conditions on the lengths of the conjugacy classes of a finite group G influence the group structure has been studied by several authors with many results available. The purpose of this paper is to analyse the restrictions imposed by the lengths of the conjugacy classes of some elements of the factors of a finite group G = G 1G2 · · · Gr , which is the product of the pairwise mutually permutable subgroups G 1, G 2, . . . , Gr , on its structure. Some earlier results appear as corollaries of our main theorems.

Keywords: Finite groups, Mutually permutable products, Conjugacy classes.
Mathematics Subject Classification: 20D10, 20D20, 20D40, 20E45