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 “On partial CAP-subgroups of finite groups” published in J. Algebra

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

On partial CAP-subgroups of finite groups

J. Algebra, 431 (2015), 196–208

http://dx.doi.org/10.1016/j.jalgebra.2015.01.035

Abstract

Given a chief factor H/K of a finite group G, we say that a subgroup A of G avoids H/K if H∩A=K∩A; if HA=KA, then we say that A covers H/K. If A either covers or avoids the chief factors of some given chief series of G, we say that A is a partial CAP-subgroup of G. Assume that G has a Sylow p-subgroup of order exceeding pk. If every subgroup of order pk, where k≥1, and every subgroup of order 4 (when pk=2 and the Sylow 2-subgroups are non-abelian) are partial CAP-subgroups of G, then G is p-soluble of p-length at most 1.

2010 Mathematics subject classification: 20D10; 20D20

Keywords: Finite group; Partial CAP-subgroup; p-soluble group; p-length

 

Paper “A bound on the p-length of p-solvable groups” published in Glasg. Math. J.

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Jon González-Sánchez, Francesca Spagnuolo

A bound on the p-length of p-solvable groups

Glasg. Math. J., 57(1) (2015), 167–171

http://dx.doi.org/10.1017/S0017089514000196

Abstract

Let G be a finite p-solvable group and P a Sylow p-subgroup of G. Suppose that $\gamma_{\ell (p-1)}(P)\subseteq \gamma_r(P)^{p^s}$ for ℓ(p−1) < r + s(p − 1), then the p-length is bounded by a function depending on ℓ.

2010 Mathematics subject classification: primary 20D10; secondary 20D15

 

Paper “Subgroup embedding properties and the structure of finite groups” published in Note Mat.

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A. Ballester-Bolinches

Subgroup embedding properties and the structure of finite groups

Note Mat., 34(1) (2014), 35–52

http://dx.doi.org/10.1285/i15900932v34n1p35

Abstract

Our main aim in this paper is to present some results to help us better understand some different ways a subgroup can be embedded in a finite group and their impact on the group structure

2010 Mathematics subject classification: 20D10; 20D20

Keywords and phrasesfinite group; subgroup embedding property; supplements; Schunck classes; formations; hypercentral groups; p-length; p-nilpotency

Paper “On the p-length of some finite p-soluble groups” published in Israel J. Math.

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Adolfo Ballester-Bolinches, Ramón Esteban-Romero, Luis M. Ezquerro

On the p-length of some finite p-soluble groups

Israel J. Math., 204(1) (2014), 359–371

http://dx.doi.org/10.1007/s11856-014-1095-y

Abstract

The main aim of this paper is to give structural information of a finite group of minimal order belonging to a subgroup-closed class of finite groups and whose p-length is greater than 1, p a prime number. Alternative proofs and improvements of recent results about the influence of minimal p-subgroups on the p-nilpotence and p-length of a finite group arise as consequences of our study.

Paper “On the p-length of some finite p-soluble groups” to appear in Israel J. Math.

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A. Ballester-Bolinches, R. Esteban-Romero, L. M. Ezquerro

On the p-lenght of some finite p-soluble groups

Israel J. Math., in press

http://dx.doi.org/10.1007/s11856-014-1095-y

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Abstract:
The main aim of this paper is to give structural information of a finite group of minimal order belonging to a subgroup-closed class of finite groups and whose p-length is greater than 1, p a prime number. Alternative proofs and improvements of recent results about the influence of minimal p-subgroups on the p-nilpotence and p-length of a finite group
arise as consequences of our study.

Paper “On the p-length of some finite p-soluble groups” to appear in Israel J. Math.

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A. Ballester-Bolinches, R. Esteban-Romero, Luis M. Ezquerro,

On the p-length of some finite p-soluble groups

Israel J. Math.

 

Abstract

The main aim of this paper is to give structural information of a finite group of minimal order belonging to a subgroup-closed class of finite groups and whose p-length is greater than 1, p a prime number. Alternative proofs and improvements of recent results about the influence of minimal p-subgroups on the p-nilpotence and p-length of a finite group arise as consequences of our study.