Archivo de la etiqueta: residual

Paper «Generalised mutually permutable products and saturated formations» published in J. Algebra

Posted on por

The following paper has been published:
El siguiente artículo ha sido publicado:
El següent article ha sigut publicat:

A. Ballester-Bolinches, S. Y. Madanha, M. C. Pedraza-Aguilera.
Generalised mutually permutable products and saturated formations.
J. Algebra, 595:434-443, 2022.

doi: 10.1016/j.jalgebra.2021.12.027

Abstract:

We say that a group G = AB is the weakly mutually permutable product of the subgroups A and B, if A permutes with every subgroup of B containing A ∩ B and B permutes with every subgroup of A containing A ∩ B. We prove that some known results for mutually permutable products remain true for weakly mutually permutable ones. Moreover, if G‘ is nilpotent, A permutes with every Sylow subgroup of B and B permutes with every Sylow subgroup of A, we show that G^F = A^FB^F, where is F a saturated formation containing U, the class of supersoluble groups. This generalises the corresponding result on mutually permutable products.

2020 Mathematics Subject Classification: 20D10, 20D20.

Keywords: weakly mutually permutable products, saturated formations, residuals

Paper «On formations of finite groups with the generalized Wielandt property for residuals II» published in J. Algebra Appl.

Posted on por

The following paper has been published:

El siguiente artículo ha sido publicado:

El següent article ha sigut publicat:

A. Ballester-Bolinches, S. F. Kamornikov, V. Pérez-Calabuig

On formations of finite groups with the generalized Wielandt property for residuals II

J. Algebra Appl., 17 (9):1850167 (8 pages), 2018

http://dx.doi.org/10.1142/S0219498818501670

Abstract

A formation F of finite groups has the generalized Wielandt property for residuals, or F is a GWP-formation, if the F-residual of a group generated by two F-subnormal subgroups is the subgroup generated by their F-residuals. The main result of this paper describes a large family of GWP-formations to further the transparence of this kind of formations, and it can be regarded as a natural step toward the solution of the classification problem.

2010 Mathematics Subject Classification: 20D10, 20D20

Keywords: Finite group; formation; residual; subnormality.

Paper “Normalisers of residuals of finite groups” published in Arch. Math. (Basel)

Posted on por

The following paper has been published

El siguiente artículo ha sido publicado

El següent article ha sigut publicat

A. Ballester-Bolinches, S. F. Kamornikov, and H. Meng

Normalisers of residuals of finite groups

Arch. Math. (Basel), 109(4):305–310, 2017

https://doi.org/10.1007/s00013-017-1074-8

Abstract:

Let F be a subgroup-closed saturated formation of finite groups containing all finite nilpotent groups, and let M be a subgroup of a finite group G normalising the F-residual of every non-subnormal subgroup of G. We show that M normalises the F-residual of every subgroup of G. This answers a question posed by Gong and Isaacs (Arch Math 108:1–7, 2017) when F is the formation of all finite supersoluble groups.

2010 Mathematics Subject Classification: 20D10, 20D35

Keywords: Finite group, Formation, Residual, Subnormality

Paper «On formations of finite groups with the generalised Wielandt property for residuals» published in J. Algebra

Posted on por

The following paper has been published:

El siguiente artículo ha sido publicado:

El següent article ha sigut publicat:

A. Ballester-Bolinches, S. F. Kamornikov, and V. Pérez-Calabuig

On formations of finite groups with the generalised Wielandt property for residuals

J. Algebra., 412 (2014), 173–178

http://dx.doi.org/10.1007/s11856-013-0030-y

Abstract

A formation F of finite groups has the generalised Wielandt property for residuals, or F is a GWP-formation, if the F-residual of a group generated by two F-subnormal subgroups is the subgroup generated by their F-residuals. We prove that every GWP-formation is saturated. This is one of the crucial steps in the hunt for a solution of the classification problem.

2010 Mathematics subject classification: 20D10; 20D20

Keywords: finite group; formation; residual; subnormality