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

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

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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

Paper “On a problem of L.A. Shemetkov on superradical formations of finite groups” published in J. Algebra

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A. Ballester-Bolinches, S. F. Kamornikov, V. N. Tyutyanov

On a problem of L.A. Shemetkov on superradical formations of finite groups

J. Algebra, 403, 69-76 (2014)

http://dx.doi.org/10.1016/j.jalgebra.2014.01.004

Abstract: Subgroup-closed saturated formations F which are closed under taking products of F-subnormal F-subgroups are studied in the paper. Our results can be regarded as further developments in the hunt for a solution of a problem proposed by L.A. Shemetkov in 1999 in the Kourovka Notebook.

MSC: 20D10, 20D20
Keywords: Finite group, saturated formation, critical group