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 “Groups whose primary subgroups are normal sensitive” published in Monatsh. Math.

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Adolfo Ballester-Bolinches, Leonid A. Kurdachenko, Javier Otal, and Tatiana Pedraza

Groups whose primary subgroups are normal sensitive

Monatsh. Math., 175(2) (2014), 175–185

http://dx.doi.org/10.1007/s00605-013-0566-2

Abstract

A subgroup H of a group G is said to be normal sensitive in G if for every normal subgroup N of H,N=H∩NG. In this paper we study locally finite groups whose p-subgroups are normal sensitive. We show the connection between these groups and groups in which Sylow permutability is transitive.

2010 Mathematics subject classification: 20E07; 20E15; 20F22; 20F50

Keywords: Locally finite group; Normal sensitivity; Primary subgroup; PST-group; T-group

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.

Paper “Primitive subgroups and PST-groups” published in Bull. Aust. Math. Soc

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

Primitive groups and PST-groups

Bull. Aust. Math. Soc., 89 (2014), 373–378

http://dx.doi.org/10.1017/S0004972713000592

Abstract

All groups considered in this paper are finite. A subgroup H of a group G is called a primitive subgroup if it is a proper subgroup in the intersection of all subgroups of G containing H as a proper subgroup. He et al. [‘A note on primitive subgroups of finite groups’, Commun. Korean Math. Soc. 28(1) (2013), 55–62] proved that every primitive subgroup of G has index a power of a prime if and only if G/Φ(G) is a solvable PST-group. Let X denote the class of groups G all of whose primitive subgroups have prime power index. It is established here that a group G is a solvable PST-group if and only if every subgroup of G is an X-group.

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

Keywords and phrases: finite groups, primitive subgroups, solvable PST-groups, T0-groups

Paper “On a class of supersoluble groups” accepted for publication 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., in press

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

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Abstract: A subgroup H of a finite group G is said to be S-permutable 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: 20D10, 20D15, 20D20

Keywords: Finite group, soluble PST-group, T_0-group, MS-group, BT-group.

Paper “Some subgroup embeddings in finite groups” accepted for publication 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

J. Adv. Res., in press

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

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

2010 Mathematics subject classification:

20D05, 20D10, 20F16

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

 

Paper “On the abnormal structure of finite groups” published in Revista Matemática Iberoamericana

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Adolfo Ballester-Bolinches, John Cossey, Ramón Esteban-Romero

On the abnormal structure of finite groups

Rev. Mat. Iberoamericana., 30, 13-24 (2014)

http://dx.doi.org/10.4171/rmi/767

Abstract: We study finite groups in which every maximal subgroup is supersoluble or normal. Our results answer some questions arising from papers of Asaad and Rose.


MSC: 20D10, 20D05, 20F16
Keywords: Finite group, supersoluble group, maximal subgroup