Paper “Some Results on Products of Finite Groups” published in Bull. Malays. Math. Sci. Soc.

The following paper has been published

El siguiente artículo ha sido publicado

El següent article ha sigut publicat

Adolfo Ballester-Bolinches, Luis M. Ezquerro, A. A. Heliel, and M. M. Al-Shomrani

Some results on products of finite groups

Bull. Malays. Math. Sci. Soc., 40(3):1341–1351, 2017

https://doi.org/10.1007/s40840-015-0111-7

Abstract

Subgroups A and B of a finite group are said to be mutually permutable (respectively, M-permutable and sn-permutable) if A permutes with every subgroup (respectively, every maximal subgroup and every subnormal subgroup) of B and viceversa. If every subgroup of A permutes with every subgroup of B, then the product is said to be totally permutable. These kinds of products have received much attention in the last twenty years. The aim of this paper is to analyse the behaviour of finite pairwise mutually permutable, mutually M-permutable, mutually sn-permutable and totally permutable products with respect to certain classes of groups including the supersoluble groups, widely supersoluble groups, and also the classes of PST-, PT– and T-groups.

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

Keywords: Finite group, Permutability, Products of groups,  Supersoluble group

 

 

 

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

The following paper has been published

El siguiente artículo ha sido publicado

El següent article ha sigut publicat

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 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 -permutable if H permutes with all members of . The main goal of this paper is to study the embedding of the -permutable subgroups and the influence of -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