Archivo por meses: abril 2016

Paper “On generalised FC-groups in which normality is a transitive relation” published in J. Aust. Math. Soc.

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R. Esteban-Romero and G. Vincenzi.

On generalised FC-groups in which normality is a transitive relation.

 J. Aust. Math. Soc., 100(2):192–198, 2016

https://doi.org/10.1017/S1446788715000397

Abstract

We extend to soluble FC-groups, the class of generalised FC-groups introduced in de Giovanni et al. [‘Groups with restricted conjugacy classes’, Serdica Math. J. 28(3) (2002), 241–254], the characterisation of finite soluble T-groups obtained recently in Kaplan [‘On T-groups, supersolvable groups, and maximal subgroups’, Arch. Math. (Basel) 96(1) (2011), 19–25].

2010 Mathematical Subject Classification: Primary 20F24; Secondary 20E34, 20F14, 20F19

Paper “A note on a result of Guo and Isaacs about p-supersolubility of finite groups” published in Arch. Math. (Basel)

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Adolfo Ballester-Bolinches, Ramón Esteban-Romero, and ShouHong Qiao.

A note on a result of Guo and Isaacs about p-supersolubility of finite groups.

Arch. Math. (Basel), 106(6):501–506, 2016.

https://doi.org/10.1007/s00013-016-0901-7

Abstract

In this note, global information about a finite group is obtained by assuming that certain subgroups of some given order are S-semipermutable. Recall that a subgroup H of a finite group G is said to be S-semipermutable if H permutes with all Sylow subgroups of G of order coprime to |H|. We prove that for a fixed prime p, a given Sylow p-subgroup P of a finite group G, and a power d of p dividing |G| such that 1≤d<|P|, if H∩O^p(G) is S-semipermutable in O^p(G) for all normal subgroups H of P with |H|=d, then either G is p-supersoluble or else |P∩O^p(G)|>d. This extends the main result of Guo and Isaacs in (Arch. Math. 105:215–222 2015). We derive some theorems that extend some known results concerning S-semipermutable subgroups.

2010 Mathematical Subject Classification: 20D10, 20D20

Keywords: Finite group, p-supersoluble group, S-semipermutable subgroup

Paper “Z-permutable subgroups of finite groups” published in Monatsh. Math.

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A. A. Heliel, A. Ballester-Bolinches, R. Esteban-Romero, and M. O. Almestady.

Ζ-permutable subgroups of finite groups.

Monatsh. Math., 179(4):523–534, 2016

https://doi.org/10.1007/s00605-015-0756-1

Abstract

Let ℨ be a complete set of Sylow subgroups of a finite group G, that is, a set composed of a Sylow p-subgroup of G for each p dividing the order of G. A subgroup H of G is called ℨ-permutable if H permutes with all members of ℨ. The main goal of this paper is to study the embedding of the ℨ-permutable subgroups and the influence of ℨ-permutability on the group structure.

2010 Mathematics Subject Classification: 20D10, 20D20, 20D35, 20D40

Keywords: Finite group, p-soluble group, p-supersoluble, ℨ-permutable subgroup, Subnormal subgroup