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 note on solubly saturated formations of finite groups” published in J. Algebra Appl.

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A. Ballester-Bolinches, S. F. Kamornikov

A note on solubly saturated formations of finite groups

J. Algebra Appl., 14(4) (2015), 1550047, 4

http://dx.doi.org/10.1142/S0219498815500474

Abstract

The main aim of this note is to give a criterion for a subgroup-closed formation to be solubly saturated, which we hope may provide a useful proving ground for outstanding questions about this family of formations.

Read More: http://www.worldscientific.com/doi/10.1142/S0219498815500474

2010 Mathematics subject classification20D10, 20D20

KeywordsFinite group; formation; saturation; soluble saturation

Paper “Some subgroup embeddings in finite groups: A mini-review” published in J. Adv. Res.

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A. Ballester-Bolinches, J. C. Beidleman, R. Esteban-Romero, M. F. Ragland

Some subgroup embeddings in finite groups: A mini-review

J. Adv. Res., 6(3) (2015), 359–362

http://dx.doi.org/10.1016/j.jare.2014.04.004

Abstract

In this survey paper several subgroup embedding properties related to some types of permutability are introduced and studied.

Keywords and phrases: Finite group; Permutability; S-permutability; Semipermutability; Primitive subgroup; Quasipermutable subgroup

Paper “On a class of generalised Schmidt groups” published in Ann. Mat. Pura Appl.

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A. Ballester-Bolinches, R. Esteban-Romero, Qinhui Jiang, and Xianhua Li

On a class of generalised Schmidt groups

Ann. Mat. Pura Appl. (4), 194(1) (2015), 77–86

http://dx.doi.org/10.1007/s10231-013-0365-3

Abstract

In this paper families of non-nilpotent subgroups covering the non-nilpotent part of a finite group are considered. An A_5-free group possessing one of these families is soluble, and soluble groups with this property have Fitting length at most three. A bound on the number of primes dividing the order of the group is also obtained.

2010 Mathematics subject classification: 20D05; 20D10; 20F16

Keywords: finite groups; nilpotent groups; maximal subgroups

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 a class of supersoluble groups” published in Bull. Aust. Math. Soc.

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A. Ballester-Bolinches, J. C. Beidleman, R. Esteban-Romero, M. F. Ragland

On a class of supersoluble groups

Bull. Aust. Math. Soc., 90 (2014), 220–226

http://dx.doi.org/10.1017/S0004972714000306

Abstract

A subgroup H of a finite group G is said to be S-semipermutable in G if H permutes with every Sylow q-subgroup of G for all primes q not dividing |H|. A finite group G is an MS-group if the maximal subgroups of all the Sylow subgroups of G are S-semipermutable in G. The aim of the present paper is to characterise the finite MS-groups.

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

Keywords and phrases: finite group; soluble PST-group; T0-group; MS-group; BT-group

Paper “On generalised pronormal subgroups of finite groups” published in Glasgow Math. J.

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A. Ballester-Bolinches, J. C. Beidleman, A. D. Feldman, M. F. Ragland

On generalised pronormal subgroups of finite groups

Glasgow Math. J., 56(3) (2014), 691–703

http://dx.doi.org/10.1017/S0017089514000159

Abstract

For a formation $\mathfrak F$, a subgroup M of a finite group G is said to be $\mathfrak F$-pronormal in G if for each g ∈ G, there exists x ∈ 〈U,Ug $\mathfrak F$ such that Ux = Ug . Let f be a subgroup embedding functor such that f(G) contains the set of normal subgroups of G and is contained in the set of Sylow-permutable subgroups of G for every finite group G. Given such an f, let fT denote the class of finite groups in which f(G) is the set of subnormal subgroups of G; this is the class of all finite groups G in which to be in f(G) is a transitive relation in G. A subgroup M of a finite group G is said to be $\mathfrak F$-normal in G if G/Core G(M) belongs to $\mathfrak F$. A subgroup U of a finite group G is called K-$\mathfrak F$-subnormal in G if either U = G or there exist subgroups U = U 0U 1 ≤ . . . ≤ Un = G such that Ui–1 is either normal or $\mathfrak F$-normal in Ui , for i = 1,2, …, n. We call a finite group G an $fT_{\mathfrak F}$-group if every K-$\mathfrak F$-subnormal subgroup of G is in f(G). In this paper, we analyse for certain formations $\mathfrak F$ the structure of $fT_{\mathfrak F}$-groups. We pay special attention to the $\mathfrak F$-pronormal subgroups in this analysis.

2010 Mathematics subject classification: 20D10; 20D35; 20F17

Paper “On formations of finite groups with the generalised Wielandt property for residuals” published in J. Algebra

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A. Ballester-Bolinches, S. F. Kamornikov, and V. Pérez-Calabuig

On formations of finite groups with the generalised Wielandt property for residuals

J. Algebra., 412 (2014), 173–178

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

Abstract

A formation F of finite groups has the generalised Wielandt property for residuals, or F is a GWP-formation, if the F-residual of a group generated by two F-subnormal subgroups is the subgroup generated by their F-residuals. We prove that every GWP-formation is saturated. This is one of the crucial steps in the hunt for a solution of the classification problem.

2010 Mathematics subject classification: 20D10; 20D20

Keywords: finite group; formation; residual; subnormality

Paper “On the intersection of certain maximal subgroups of a finite group” published in J. Group Theory

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Adolfo Ballester-Bolinches, James C. Beidleman, Hermann Heineken, Matthew F. Ragland, Jack Schmidt

On the intersection of certain maximal subgroups of a finite group

J. Group Theory, 17 (2014), 705–715

http://dx.doi.org/10.1515/jgt-2013-0052

Abstract:  Let $\Delta(G)$ denote the intersection of all non-normal maximal subgroups of a group G. We introduce the class of T2-groups which are defined as the groups G for which $G/\Delta(G)$ is a T-group, that is, a group in which normality is a transitive relation. Several results concerning the class T2 are discussed. In particular, if G is a solvable group, then Sylow permutability is a transitive relation in G if and only if every subgroup H of G is a T2-group such that the nilpotent residual of H is a Hall subgroup of H.