Archivo de la etiqueta: J. Group Theory

Paper «On a class of finite soluble groups» published in J. Group Theory

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A. Ballester-Bolinches, John Cossey, Yangming Li.
On a class of finite soluble groups.
J. Group Theory, 21(5):839-846 2018.

doi: 10.1515/jgth-2018-0015

Abstract:

The aim of this paper is to study the class of finite groups in which every subgroup is self-normalising in its subnormal closure. It is proved that this class is a subgroup-closed formation of finite soluble groups which is not closed under taking Frattini extensions and whose members can be characterised by means of their Carter subgroups. This leads to new characterisations of finite soluble T-, PT- and PST-groups. Finite groups whose p-subgroups, p a prime, are self-normalising in their subnormal closure are also characterised.

Paper «On the intersection of certain maximal subgroups of a finite group» published in J. Group Theory

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The following paper has been published.

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Adolfo Ballester-Bolinches, James C. Beidleman, Hermann Heineken, Matthew F. Ragland, Jack Schmidt

On the intersection of certain maximal subgroups of a finite group

J. Group Theory, 17 (2014), 705–715

http://dx.doi.org/10.1515/jgt-2013-0052

Abstract:  Let $\Delta(G)$ denote the intersection of all non-normal maximal subgroups of a group G. We introduce the class of T2-groups which are defined as the groups G for which $G/\Delta(G)$ is a T-group, that is, a group in which normality is a transitive relation. Several results concerning the class T2 are discussed. In particular, if G is a solvable group, then Sylow permutability is a transitive relation in G if and only if every subgroup H of G is a T2-group such that the nilpotent residual of H is a Hall subgroup of H.

Paper «On the intersection of certain maximal subgroups of a finite group» to appear in J. Group Theory

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The following paper has been accepted for publication.

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Adolfo Ballester-Bolinches, James C. Beidleman, Hermann Heineken, Matthew F. Ragland, Jack Schmidt

On the intersection of certain maximal subgroups of a finite group

J. Group Theory, in press

http://dx.doi.org/10.1515/jgt-2013-0052

Abstract:  Let $\Delta(G)$ denote the intersection of all non-normal maximal subgroups of a group G. We introduce the class of T2-groups which are defined as the groups G for which $G/\Delta(G)$ is a T-group, that is, a group in which normality is a transitive relation. Several results concerning the class T2 are discussed. In particular, if G is a solvable group, then Sylow permutability is a transitive relation in G if and only if every subgroup H of G is a T2-group such that the nilpotent residual of H is a Hall subgroup of H.