Archivo de la etiqueta: Ning su

Paper “On the focal subgroup of a saturated fusion system” published in J. Algebra

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Adolfo Ballester-Bolinches, Luis M. Ezquerro, Ning Su, and Yanming Wang.

On the focal subgroup of a saturated fusion system.

J. Algebra, 468:72–79, 2016

https://doi.org/10.1016/j.jalgebra.2016.07.034

Abstract

The influence of the cyclic subgroups of order p or 4 of the focal subgroup of a saturated fusion system F over a p-group S is investigated in this paper. Some criteria for normality of S in F as well as necessary and sufficient conditions for nilpotency of F are given. The resistance of a p-group in which every cyclic subgroup of order p or 4 is normal, and earlier results about p-nilpotence of finite groups and nilpotency of saturated fusion systems are consequences of our study.

2010 Mathematical Subject Classification: 20C20

Keywords: Saturated fusion system, Control of fusion

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 bounds for the p-length of finite p-soluble groups” published in Collect. Math.

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The following paper has been published

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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 “On π-S-permutable subgroups of finite groups” published in Mediterr. J. Math.

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A. Ballester-Bolinches, Yangming Li, Ning Su, and Zhuoqing Xie.

On π-S-permutable subgroups of finite groups.

 Mediterr. J. Math., 13(1):93–99, 2016

https://doi.org/10.1007/s00009-014-0479-x

Abstract

Let π be a set of primes. A subgroup H of a finite group G is said to be π-S-permutable in G if H permutes with every Sylow q-subgroup of G for all primes q ∈ π. The main aim of this paper is to establish structural results about the normal closure of π-S-permutable subgroups and p-subgroups permuting with all p′-subgroups for a single prime p. Our results stem from a recent article by Isaacs and subsequent discussions with the authors about it.

2010 Mathematics Subject Classification: Primary 20D10; Secondary 20D15, 20D20, 20D40

Keywords: Finite group, Permutability, S-permutability, S-semipermutability, Normal closure