Paper “On two classes of finite supersoluble groups” published in Comm. Algebra

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W. M. Fakieh, R. A. Hijazi, A. Ballester-Bolinches, J. C. Beidleman

On two classes of finite supersoluble groups

Comm. Algebra., 46 (3):1110-1115, 2018

doi:10.22108/ijgt.2017.21214

Abstract

Let Z 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 Z-S-semipermutable if H permutes with every Sylow p-subgroup of G in Z for all p not in π(H); H is said to be Z-S-seminormal if it is normalized by every Sylow p-subgroup of G in Z for all p not in π(H). The main aim of this paper is to characterize the Z-MS-groups, or groups G in which the maximal subgroups of every Sylow subgroup in Z are Z-S-semipermutable in G and the Z-MSN-groups, or groups in which the maximal subgroups of every Sylow subgroup in Z are Z-S-seminormal in G.

2010 Mathematics Subject Classification: 20D10; 20D20; 20D35; 20D40

Keywords: Finite group; permutability; soluble group; supersoluble group; Sylow sets

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 “A Note on Solitary Subgroups of Finite Groups” published in Comm. Algebra

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R. Esteban-Romero and Orieta Liriano

A note on solitary subgroups of finite groups.

Comm. Algebra, 44(7):2945–2952, 2016

https://doi.org/10.1080/00927872.2015.1065855

Abstract

We say that a subgroup H of a finite group G is solitary (respectively, normal solitary) when it is a subgroup (respectively, normal subgroup) of G such that no other subgroup (respectively, normal subgroup) of G is isomorphic to H. A normal subgroup N of a group G is said to be quotient solitary when no other normal subgroup K of G gives a quotient isomorphic to G/N. We show some new results about lattice properties of these subgroups and their relation with classes of groups and present examples showing a negative answer to some questions about these subgroups.

2010 Mathematics Subject Classification: 20D10, 20D30, 20F16

Keywords: Finite group, Fitting class, Formation, Quotient solitary subgroup, Solitary subgroup