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.

Paper “On conjugacy of supplements of normal subgroups of finite groups” published in Bull. Austral. Math. Soc.

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A. Ballester-Bolinches, L. M. Ezquerro

On conjugacy of supplements of normal subgroups of finite groups

Bull. Aust. Math. Soc., 89 (2014), 293–299

http://dx.doi.org/10.1017/S0004972713000506

Abstract

The objective of this paper is to find some sufficient conditions to ensure the conjugacy of supplements of a normal subgroup of a soluble group.

2010 Mathematics subject classification: primary 20D10; secondary 20D15, 20D20

Keywords and phrasesfinite groups, supplements, Schunck classes, formations

Paper “On subgroups of hypercentral type of finite groups” published in Israel J. Math.

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A. Ballester-Bolinches, Luis M. Ezquerro, Alexander N. Skiba

On subgroups of hypercentral type of finite groups

Israel J. Math., 199 (2014), 259–265

http://dx.doi.org/10.1007/s11856-013-0030-y

Abstract

The main purpose of this paper is to analyze the influence on the structure of a finite group of some subgroups lying in the hypercenter. More precisely, we prove the following: Let

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.

Paper “On conjugacy of supplements of normal subgroups of finite groups” to appear in Bull. Aust. Math. Soc.

The following paper has been accepted for publication. We will inform about the bibliographical details.

El siguiente artículo ha sido aceptado para su publicación. Informaremos sobre los detalles bibliográficos.

El següent article ha sigut acceptat per a la seua publicació. N’informarem sobre els detalls bibliogràfics.

A. Ballester-Bolinches, Luis M. Ezquerro,

On conjugacy of supplements of normal subgroups of finite groups

Bull. Aust. Math. Soc.

http://dx.doi.org/10.1017/S0004972713000506

Abstract: The objective of this paper is to find some sufficient conditions to ensure the conjugacy of supplements of a normal subgroup of a soluble group.

2010 Mathematics subject classification: primary 20D10; secondary 20D20.
Keywords and phrases: finite groups, supplements, Schunck classes, formations.

Paper “On subgroups of hypercentral type of finite groups” to appear in Israel J. Math.

The following paper has been accepted for publication. We will inform about the bibliographical details.

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A. Ballester-Bolinches, Luis M. Ezquerro, Alexander N. Skiba

On subgroups of hypercentral type of finite groups

Israel J. Math.

http://dx.doi.org/10.1007/s11856-013-0030-y

Abstract

The main purpose of this paper is to analyze the influence on the structure of a finite group of some subgroups lying in the hypercenter. More precisely, we prove the following: Let F be a Baer-local formation. Given a group G and a normal subgroup E of G, let ZF (G) contain a p-subgroup A of E which is maximal being abelian and of exponent dividing pk, where k is some natural number, k = 1 if p = 2 and the Sylow 2-subgroups of E are non-abelian. Then E/ O p (E) ≤ ZF(G/ Op (E)) (Theorem 1). Some well-known results turn out to be consequences of this theorem.