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

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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 “Finite groups with all minimal subgroups solitary” published in J. Algebra Appl.

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R. Esteban-Romero and Orieta Liriano.

Finite groups with all minimal subgroups solitary.

J. Algebra Appl., 15(8):1650140, 9, 2016

https://doi.org/10.1142/S0219498816501401

Abstract 

We give a complete classification of the finite groups with a unique subgroup of order p for each prime p dividing its order.

2010 Mathematical Subject Classification: 20D10, 20D30

Keywords: Finite group; solitary subgroup; minimal subgroup

Paper “A note on solubly saturated formations of finite groups” published in J. Algebra Appl.

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A. Ballester-Bolinches, S. F. Kamornikov

A note on solubly saturated formations of finite groups

J. Algebra Appl., 14(4) (2015), 1550047, 4

http://dx.doi.org/10.1142/S0219498815500474

Abstract

The main aim of this note is to give a criterion for a subgroup-closed formation to be solubly saturated, which we hope may provide a useful proving ground for outstanding questions about this family of formations.

Read More: http://www.worldscientific.com/doi/10.1142/S0219498815500474

2010 Mathematics subject classification20D10, 20D20

KeywordsFinite group; formation; saturation; soluble saturation