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 “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.

The following paper has been published.

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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/