Archivo de la etiqueta: p-nilpotency

Paper «On a paper of Beltrán and Shao about coprime action» published in J. Pure Appl. Algebra

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H. Meng and A. Ballester-Bolinches.
On a paper of Beltrán and Shao about coprime action.
J. Pure Appl. Algebra, 224(8):106313, 4, 2020.

doi:10.1016/j.jpaa.2020.106313

Abstract

Assume that A and G are finite groups of coprime orders such that A acts on G via automorphisms. Let p be a prime. The following coprime action version of a well-known theorem of Itô about the structure of a minimal non-p-nilpotent groups is proved: if every maximal A-invariant subgroup of G is p-nilpotent, then G is p-soluble. If, moreover, G is not p-nilpotent, then G must be soluble. Some earlier results about coprime action are consequences of this theorem.

2020 Mathematics Subject Classification: 20D10, 20D25

Keywords: finite groups; coprime action; solubility; p-nilpotency

Paper “On finite p-nilpotent groups” published in Monatsh. Math.

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Adolfo Ballester-Bolinches, Xiuyun Guo, Yangming Li, and Ning Su.

On finite p-nilpotent groups.

Monatsh. Math., 181(1):63–70, 2016

https://doi.org/10.1007/s00605-015-0803-y

Abstract

In this paper the structure of a minimal counterexample among the non-p-nilpotent groups having p-nilpotent p-Sylow normalisers is analysed. Several p-nilpotency criteria and many earlier results follow from our main theorem.

2010 Mathematics Subject Classification: 20D10, 20D20

Keywords: Finite groups, p-nilpotency, Minimal subgroups, Sylow normalisers

Paper «On p-nilpotency of hyperfinite groups» published in Monatsh. Math.

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A. Ballester-Bolinches, S. Camp-Mora, and F. Spagnuolo

On p-nilpotency of hyperfinite groups

Monatsh. Math., 176(4) (2015), 497–502

http://dx.doi.org/10.1007/s00605-014-0633-3

Abstract

Let p be a prime. We say that class X of hyperfinite p-groups determines p-nilpotency locally if every finite group G with a Sylow p-subgroup P in X is p-nilpotent if and only if N_G(P) is p-nilpotent. The results of this paper improve a recent result of Kurdachenko and Otal and show that if a hyperfinite group G has a pronormal Sylow p-subgroup in X, then G is p-nilpotent if and only if N_G(P) is p-nilpotent provided that X is closed under taking subgroups and epimorphic images. If X is not closed under taking epimorphic images, we have to impose local p-solubility to G. In this case, the hypothesis of pronormality can be removed.

2010 Mathematics subject classification: 20E15, 20F19, 20F22

Keywords: locally finite group; hyperfinite group; p-nilpotency

Paper «Subgroup embedding properties and the structure of finite groups» published in Note Mat.

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The following paper has been published:

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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 phrases: finite 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» to appear in Israel J. Math.

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

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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.