Paper “On complements of F-residuals of finite groups” published in Comm. Algebra

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

On Complements of F-residuals of finite groups

Comm. Algebra, 45(2):878–882, 2017.

https://doi.org/10.1080/00927872.2016.1175615

Abstract

A formation F of finite groups has the generalized Wielandt property for residuals, or 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 aim of the paper is to determine some sufficient conditions for a finite group to split over its F-residual.

2010 Mathematics subject classification: 20D10; 20D20

Keywords: Finite group; formation; residual; subnormality

Paper “On seminormal subgroups of finite groups” published in Rocky Mountain J. Math.

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A. Ballester-Bolinches, J. C. Beidleman, V. Pérez-Calabuig, and M. F. Ragland

On seminormal subgroups of finite groups

Rocky Mountain J. Math., 47(2):419–427, 2017

https://doi.org/10.1216/RMJ-2017-47-2-419

Abstract

All groups considered in this paper are finite. A subgroup H of a group G is said to be seminormal in G if H is normalized by all subgroups K of G such that gcd(|H|,|K|)=1 . We call a group G an MSN-group if the maximal subgroups of all the Sylow subgroups of G are seminormal in G. In this paper, we classify all MSN-groups.

2010 Mathematics Subject Classification: 20D10, 20D15, 20D20

Keywords: Finite group, soluble PST-group,T₀-group, MS-group, MSN-group

 

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

The following paper has been published:

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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

Publication data for “Maximal subgroups and PST-groups” in Cent. Eur. Math. J.

Central European Journal of MathematicsWe now have the issue and page numbers for the paper we mentioned in http://permut.blogs.uv.es/2013/03/15/paper-maximal-subgroups-and-pst-groups/.

Adolfo Ballester-Bolinches, James C. Beidleman, Ramón Esteban-Romero, Vicent Pérez-Calabuig

Maximal subgroups and PST-groups

Centr. Eur. J. Math., 11(6), 2013, 1078-1082,

available on http://dx.doi.org/10.2478/s11533-013-0222-z.

Abstract:

A subgroup H of a group G is said to permute with a subgroup K of G if HK is a subgroup of G. H is said to be permutable (resp. S-permutable) if it permutes with all the subgroups (resp. Sylow subgroups) of G. Finite groups in which permutability (resp. S-permutability) is a transitive relation are called PT-groups (resp. PST-groups). PT-, PST- and T-groups, or groups in which normality is transitive, have been extensively studied and characterised. Kaplan [Kaplan G., On T-groups, supersolvable groups, and maximal subgroups, Arch. Math. (Basel), 2011, 96(1), 19–25] presented some new characterisations of soluble T-groups. The main goal of this paper is to establish PT- and PST-versions of Kaplan’s results, which enables a better understanding of the relationships between these classes.

MSC:  20D05, 20D10, 20E15, 20E28, 20F16
Keywords: Finite groups • Permutability • Sylow-permutability • Maximal subgroups • Supersolubility

(c) Versita Sp. z. o. o. and Springer

 

Paper “Maximal subgroups and PST-groups” to appear in Cent. Eur. Math. J.

Central European Journal of MathematicsThe paper

Adolfo Ballester-Bolinches, James C. Beidleman, Ramón Esteban-Romero, Vicent Pérez-Calabuig

Maximal subgroups and PST-groups

Centr. Eur. J. Math., in press

is now available on http://dx.doi.org/10.2478/s11533-013-0222-z.

Abstract:

A subgroup H of a group G is said to permute with a subgroup K of G if HK is a subgroup of G. H is said to be permutable (resp. S-permutable) if it permutes with all the subgroups (resp. Sylow subgroups) of G. Finite groups in which permutability (resp. S-permutability) is a transitive relation are called PT-groups (resp. PST-groups). PT-, PST- and T-groups, or groups in which normality is transitive, have been extensively studied and characterised. Kaplan [Kaplan G., On T-groups, supersolvable groups, and maximal subgroups, Arch. Math. (Basel), 2011, 96(1), 19–25] presented some new characterisations of soluble T-groups. The main goal of this paper is to establish PT- and PST-versions of Kaplan’s results, which enables a better understanding of the relationships between these classes.

MSC:  20D05, 20D10, 20E15, 20E28, 20F16
Keywords: Finite groups • Permutability • Sylow-permutability • Maximal subgroups • Supersolubility

(c) Versita Sp. z. o. o. and Springer

We will inform about the volume and issue this paper is officially published.