Paper “On the Prüfer rank of mutually permutable products of abelian groups” published in Ann. Mat. Pura Appl.

The following paper has been published:
El siguiente artículo ha sido publicado:
El següent article ha sigut publicat:

A. Ballester-Bolinches, J. Cossey, H. Meng, M. C. Pedraza-Aguilera.
On the Prüfer rank of mutually permutable products of abelian groups
Ann. Mat. Pura Appl. (4), 198(3):811–819, 2019.

doi:10.1007/s10231-018-0800-6

Abstract

A group G has finite (or Prüfer or special) rank if every finitely generated subgroup of G can be generated by r elements and r is the least integer with this property. The aim of this paper is to prove the following result: assume that G=AB is a group which is the mutually permutable product of the abelian subgroups A and B of Prüfer ranks r and s, respectively. If G is locally finite, then the Prüfer rank of G is at most r+s+3. If G is an arbitrary group, then the Prüfer rank of G is at most r+s+4.

2010 Mathematics Subject Classification: 20D10, 20D20

Keywords: Abelian group · Soluble group · Polycyclic group · Rank · Factorisations

Paper “Left braces and the quantum Yang-Baxter equation” published in Proc. Edinburgh Math. Soc.

The following paper has been published:
El siguiente artículo ha sido publicado:
El següent article ha sigut publicat:

H. Meng, A. Ballester-Bolinches y R. Esteban-Romero.
Left braces and the quantum Yang-Baxter equation.
Proc. Edinburgh Math. Soc., 62(2):595–608, 2019.

doi:10.1017/S0013091518000664

Abstract

Braces were introduced by Rump in 2007 as a useful tool in the study of the set-theoretic solutions of the Yang–Baxter equation. In fact, several aspects of the theory of finite left braces and their applications in the context of the Yang–Baxter equation have been extensively investigated recently. The main aim of this paper is to introduce and study two finite brace theoretical properties associated with nilpotency, and to analyse their impact on the finite solutions of the Yang–Baxter equation.

2010 Mathematics Subject Classification: 26T25, 20F16

Keywords: p-nilpotent group, braces, Yang-Baxter equation

Paper “On products of generalised supersoluble finite groups” published in Mediterr. J. Math.

The following paper has been published:
El siguiente artículo ha sido publicado:
El següent article ha sigut publicat:

A. Ballester-Bolinches, J. Cossey, H. Meng, M. C. Pedraza-Aguilera.
On products of generalised supersoluble finite groups
Ann. Mat. Pura Appl. (4), 198(3):811–819, 2019.

doi:10.1007/s10231-018-0800-6

Abstract

In this paper, mutually sn-permutable subgroups of groups belonging to a class of generalised supersoluble groups are studied. Some analogs of known theorems on mutually sn-permutable products are established.

2010 Mathematics Subject Classification: 20D10, 20D20

Keywords: Finite group, supersoluble group, Sn-permutability, factorisation

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

The following paper has been published:

El siguiente artículo ha sido publicado:

El següent article ha sigut publicat:

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 two questions from the Kourovka Notebook” published in J. Algebra

The following paper has been published:

El siguiente artículo ha sido publicado:

El següent article ha sigut publicat:

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

The following paper has been published

El siguiente artículo ha sido publicado

El següent article ha sigut publicat

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