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 “Some Results on Products of Finite Groups” published in Bull. Malays. Math. Sci. Soc.

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Adolfo Ballester-Bolinches, Luis M. Ezquerro, A. A. Heliel, and M. M. Al-Shomrani

Some results on products of finite groups

Bull. Malays. Math. Sci. Soc., 40(3):1341–1351, 2017

https://doi.org/10.1007/s40840-015-0111-7

Abstract

Subgroups A and B of a finite group are said to be mutually permutable (respectively, M-permutable and sn-permutable) if A permutes with every subgroup (respectively, every maximal subgroup and every subnormal subgroup) of B and viceversa. If every subgroup of A permutes with every subgroup of B, then the product is said to be totally permutable. These kinds of products have received much attention in the last twenty years. The aim of this paper is to analyse the behaviour of finite pairwise mutually permutable, mutually M-permutable, mutually sn-permutable and totally permutable products with respect to certain classes of groups including the supersoluble groups, widely supersoluble groups, and also the classes of PST-, PT– and T-groups.

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

Keywords: Finite group, Permutability, Products of groups,  Supersoluble group

 

 

 

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 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 “On the supersoluble hypercentre of a finite group” published in Monatsh. Math.

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Liyun Miao, Adolfo Ballester-Bolinches, Ramón Esteban-Romero, and Yangming Li

On the supersoluble hypercentre of a finite group

Monatsh. Math., 184(4):641–648, 2017

https://doi.org/10.1515/forum-2016-0262

Abstract

A subgroup H of a group G is called Sylow permutable, or S-permutable, in G if H permutes with all Sylow p-subgroups of G for all primes p. A group G is said to be a PST-group if Sylow permutability is a transitive relation in G. We show that a group G which is factorised by a normal subgroup and a subnormal PST-subgroup of odd order is supersoluble. As a consequence, the normal closure S^G of a subnormal PST-subgroup S of odd order of a group G is supersoluble, and the subgroup generated by subnormal PST-subgroups of G of odd order is supersoluble as well.

2010 Mathematics Subject Classification: 20D10, 20D20

Keywords: Finite group, p-Supersoluble group, S-semipermutable subgroup

Paper “On hall subnormally embedded subgroups of finite groups” published in Monatsh. Math.

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Adolfo Ballester-Bolinches, John Cossey, and ShouHong Qiao.

On Hall subnormally embedded subgroups of finite groups.

Monatsh. Math., 181(4):753–760, 2016

https://doi.org/10.1007/s00605-015-0838-0

Abstract

A subgroup H of a finite group G is said to be Hall subnormally (respectively normally) embedded in G if there is a subnormal (respectively normal) subgroup N of G such that H is a Hall subgroup of N. The aim of this paper is to characterise the groups G having a Hall subnormally embedded subgroup of order |B| for each subgroup B of G. Some earlier results are consequences of our main theorem.

2010 Mathematical Subject Classification: 20D10 20D20

Keywords: Finite group, Soluble group, Hall subgroup, Subnormal subgroup

Paper “On the exponent of mutually permutable products of two abelian groups” published in J. Algebra

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A. Ballester-Bolinches, John Cossey, and M. C. Pedraza-Aguilera.

On the exponent of mutually permutable products of two abelian groups.

J. Algebra, 466:34–43, 2016.

https://doi.org/10.1016/j.jalgebra.2016.05.027

Abstract

In this paper we obtain some bounds for the exponent of a finite group, and its derived subgroup, which is a mutually permutable product of two abelian subgroups. They improve the ones known for products of finite abelian groups, and they are used to derive some interesting structural properties of such products.

2010 Mathematical Subject Classification: 20D10, 20D20

Keywords: Finite group, Abelian group, Exponent, Factorisations, p-Supersolubility, p-Length

Paper “On bounds for the p-length of finite p-soluble groups” published in Collect. Math.

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Adolfo Ballester-Bolinches, Luis M. Ezquerro, and Ning Su.

On bounds for the p-length of finite p-soluble groups.

Collect. Math., 67(3):373–378, 2016.

https://doi.org/10.1007/s13348-015-0144-0

Abstract

The aim of this paper is to obtain a bound for the p-length of a p-soluble group G whose elements of order p or order 4 (if p=2) of a Sylow p-subgroup of a residual subgroup of G are contained in the k-th term of the upper central series of a Sylow p-subgroup of G.

2010 Mathematics Subject Classification: 20D10, 20D20

Keywords: Finite group, p-soluble group, p-length

Paper “Triple Factorizations and Supersolubility of Finite Groups” published on Proc. Edinb. Math. Soc.

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Adolfo Ballester-Bolinches and Luis M. Ezquerro.

Triple factorizations and supersolubility of finite groups.

Proc. Edinb. Math. Soc. (2), 59(2):301–309, 2016.

https://doi.org/10.1017/S0013091515000231

Abstract

In this paper we analyse the structure of a finite group of minimal order among the finite non-supersoluble groups possessing a triple factorization by supersoluble subgroups of pairwise relatively prime indices. As an application we obtain some sufficient conditions for a triple factorized group by supersoluble subgroups of pairwise relatively prime indices to be supersoluble. Many results appear as consequences of our analysis.

Keywords: Finite group, Supersoluble group, Factorization