Archivo por meses: abril 2017

Paper “On S-Semipermutable Subgroups and Soluble PST-Groups” published in Mediterr. J. Math.

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

On S-semipermutable subgroups and soluble PST-groups

Mediterr. J. Math., 14(2):Art. 87, 6, 2017

https://doi.org/10.1007/s00009-017-0893-y

Abstract

All groups presented in this article are finite. Using several permutability embedding properties, a number of new characterisations of soluble PST-groups are studied.

2010 Mathematics subject classification:  20D10; 20D20; 20F16

Keywords: Finite group; Permutability; S-Semipermutability

 

Paper “On finite groups with many supersoluble subgroups” published in Arch. Math. (Basel)

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A. Ballester-Bolinches, R. Esteban-Romero, and Jiakuan Lu

On finite groups with many supersoluble subgroups

Arch. Math. (Basel), 109(1):3–8, 2017

https://doi.org/10.1007/s00013-017-1041-4

Abstract

The solubility of a finite group with less than 6 non-supersoluble subgroups is confirmed in the paper. Moreover we prove that a finite insoluble group has exactly 6 non-supersoluble subgroups if and only if it is isomorphic to A_5 or SL_2 (5). Furthermore, it is shown that a finite insoluble group has exactly 22 non-nilpotent subgroups if and only if it is isomorphic to A_5 or SL_2(5). This confirms a conjecture of Zarrin (Arch Math (Basel) 99:201–206, 2012).

2010 Mathematics Subject Classification: 20D10, 20D20

Keywords: Finite group, Supersoluble subgroup, Soluble group

 

Paper «Semipermutability in generalised soluble groups» published in Bull. Austral. Math. Soc.

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A. Ballester-Bolinches, J. C. Beidleman, R. Ialenti.
Generalised mutually permutable products and saturated formations.
Bull. Austral. Math. Soc., 95(2):219-227, 2017.

doi: 10.1017/S0004972716000885

Abstract:

Some classes of finitely generated hyperabelian groups defined in terms of semipermutability and S-semipermutability are studied in the paper. The classification of finitely generated hyperabelian groups all of whose finite quotients are PST-groups recently obtained by Robinson is behind our results. An alternative proof of such a classification is also included in the paper.

2020 Mathematics Subject Classification: 20E15, 20D40.

Keywords: generalised soluble groups, permutability, S-semipermutability.

Paper «On some permutable embeddings of subgroups of finite groups» published in Rend. Lincei Mat. Appl.

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Adolfo Ballester-Bolinches, James C. Beidleman.
On some permutable embeddings of subgroups of finite groups.
Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., 28(2):339-347, 2017.

doi: 10.4171/RLM/766

Abstract:

In this survey paper several subgroup embedding properties related to some types of permutability are introduced and studied.

2020 Mathematics Subject Classification: 20D05, 20D10, 20F16.

Keywords: Finite group, permutability, S-permutability, S-semipermutability.