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 “Z-permutable subgroups of finite groups” published in Monatsh. Math.

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A. A. Heliel, A. Ballester-Bolinches, R. Esteban-Romero, and M. O. Almestady.

Ζ-permutable subgroups of finite groups.

Monatsh. Math., 179(4):523–534, 2016

https://doi.org/10.1007/s00605-015-0756-1

Abstract

Let 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 -permutable if H permutes with all members of . The main goal of this paper is to study the embedding of the -permutable subgroups and the influence of -permutability on the group structure.

2010 Mathematics Subject Classification: 20D10, 20D20, 20D35, 20D40

Keywords: Finite group, p-soluble group, p-supersoluble, ℨ-permutable subgroup, Subnormal subgroup

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 «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.