Archivo de la etiqueta: Ballester-Bolinches

Paper «A note on normal complements for finite groups» published in Bull. Austral. Math. Soc.

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Ning Su, Adolfo Ballester-Bolinches, Hangyang Meng.

A note on normal complements for finite groups

Bull. Austral. Math. Soc., 98 (1):109-112, 2018

doi:10.1017/S0004972718000151

Abstract

Assume that G is a finite group and H is a 2-nilpotent Sylow tower Hall subgroup of G such that if x and y are G-conjugate elements of H ∩ G0 of prime order or order 4, then x and y are H-conjugate. We prove hat there exists a normal subgroup N of G such that G = HN and H ∩ N = 1.

2010 Mathematics Subject Classification: primary 20D20; secondary 20D10

Keywords: finite group, conjugation, Hall subgroup, normal complement.

Paper «On metacyclic subgroups of finite groups» published in Internat. J. Group Th.

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A. Ballester-Bolinches

On metacyclic subgroups of finite groups

Internat. J. Group Theory, 7(2):25-29, 2018

http://dx.doi.org/10.22108/ijgt.2017.21480

Abstract

The aim of this survey article is to present some structural results about of groups whose Sylow p-subgroups are metacylic (p a prime). A complete characterisation of non-nilpotent groups whose 2-generator subgroups are metacyclic is also presented.

2010 Mathematics Subject Classification: Primary: 20D20; Secondary: 20E25.

Keywords: finite group, Sylow subgroups, metacyclic groups, 2-generator groups.

Paper «On a class of finite soluble groups» published in J. Group Theory

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A. Ballester-Bolinches, John Cossey, Yangming Li.
On a class of finite soluble groups.
J. Group Theory, 21(5):839-846 2018.

doi: 10.1515/jgth-2018-0015

Abstract:

The aim of this paper is to study the class of finite groups in which every subgroup is self-normalising in its subnormal closure. It is proved that this class is a subgroup-closed formation of finite soluble groups which is not closed under taking Frattini extensions and whose members can be characterised by means of their Carter subgroups. This leads to new characterisations of finite soluble T-, PT- and PST-groups. Finite groups whose p-subgroups, p a prime, are self-normalising in their subnormal closure are also characterised.

Paper «On two questions from the Kourovka Notebook» published in J. Algebra

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A. Ballester-Bolinches, John Cossey, S. F. Kamornikov, H. Meng.

On two questions from the Kourovka Notebook

J. Algebra, 499:438-449, 2018

https://doi.org/10.1016/j.jalgebra.2017.12.014

Abstract

The aim of this paper is to give answers to some questions concerning intersections of system normalisers and prefrattini subgroups of finite soluble groups raised by the third author, Shemetkov and Vasil’ev in the Kourovka Notebook [10]. Our approach depends on results on regular orbits and it can be also used to extend a result of Mann [9] concerning intersections of injectors associated to Fitting classes.

2010 Mathematics Subject Classification: 20D10, 20D20

Keywords: Finite groups. Soluble groups. Formations. Fitting classes. Prefrattini  subgroups. Normalisers. Injectors.

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 a theorem of Kang and Liu on factorised groups» published in Bull. Austral. Math. Soc.

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A. Ballester-Bolinches, M. C. Pedraza Aguilera

On a theorem of Kang and Liu on factorised groups

Bull. Austral. Math. Soc., 97 (1):54-56, 2018

https://doi.org/10.1017/S0004972717000363

Abstract

Kang and Liu [‘On supersolvability of factorized finite groups’, Bull. Math. Sci. 3 (2013), 205–210] investigate the structure of finite groups that are products of two supersoluble groups. The goal of this note is to give a correct proof of their main theorem.

2010 Mathematics Subject Classification: primary: 20D10, secondary: 20D20, 20D40

Keywords: finite group. factorisation, supersolubility

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 “Normalisers of residuals of finite groups” published in Arch. Math. (Basel)

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A. Ballester-Bolinches, S. F. Kamornikov, and H. Meng

Normalisers of residuals of finite groups

Arch. Math. (Basel), 109(4):305–310, 2017

https://doi.org/10.1007/s00013-017-1074-8

Abstract:

Let F be a subgroup-closed saturated formation of finite groups containing all finite nilpotent groups, and let M be a subgroup of a finite group G normalising the F-residual of every non-subnormal subgroup of G. We show that M normalises the F-residual of every subgroup of G. This answers a question posed by Gong and Isaacs (Arch Math 108:1–7, 2017) when F is the formation of all finite supersoluble groups.

2010 Mathematics Subject Classification: 20D10, 20D35

Keywords: Finite group, Formation, Residual, Subnormality

Paper “On locally finite groups whose subgroups of infinite rank have some permutable property” published in Ann. Mat. Pura Appl.

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A. Ballester-Bolinches, S. Camp-Mora, M. R. Dixon, R. Ialenti, and F. Spagnuolo

On locally finite groups whose subgroups of infinite rank have some permutable property

Ann. Mat. Pura Appl. (4), 196(5):1855–1862, 2017

https://doi.org/10.1007/s10231-017-0642-7

Abstract

In this paper, we study the behavior of locally finite groups of infinite rank whose proper subgroups of infinite rank have one of the three following properties, which are generalizations of permutability: S-permutability, semipermutability and S-semipermutability. In particular, it is proved that if G is a locally finite group of infinite rank whose proper subgroups of infinite rank are S-permutable (resp. semipermutable), then G is locally nilpotent (resp. all subgroups are semipermutable). For locally finite groups whose proper subgroups of infinite rank are S-semipermutable, the same statement can be proved only for groups with min-p for every prime p. A counterexample is given for the general case.

2010 Mathematical Subject Classification: 20F19, 20F50

Keywords: Locally finite group, Section p-rank, Section rank, Special rank, Permutable, Sylow permutable, Semipermutable, S-semipermutable

 

Paper “Some Local Properties Defining T₀-Groups and Related Classes of Groups” published in Publ. Mat.

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A. Ballester-Bolinches, J. C. Beidleman, R. Esteban-Romero, and M. F. Ragland

Some local properties defining T0-groups and related classes of groups

Publ. Mat., 60(1):265–272, 2016

http://projecteuclid.org/euclid.pm/1450818490

Abstract

We call G a Hall_χ-group if there exists a normal nilpotent subgroup N of G for which G/N′ is an χ-group. We call G a T₀-group provided G/Φ(G) is a T-group, that is, one in which normality is a transitive relation. We present several new local classes of groups which locally define Hall_χ-groups and T₀-groups where χ∈{T, PT, PST}; the classes PT and PST denote, respectively, the classes of groups in which permutability and S-permutability are transitive relations.

2010 Mathematical Subject Classification: 20D10, 20D20, 20D35

Keywords: Subnormal subgroup, T-group, PST-group, finite solvable group