Paper “A note on normal complements for finite groups” published in Bull. Austral. Math. Soc.

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Ning Su, Adolfo Ballester-Bolinches, Hangyang Meng.

A note on normal complements for finite groups

Bull. Austral. Math. Soc., 98 (1):109-112, 2018

doi:10.1017/S0004972718000151

Abstract

Assume that G is a finite group and H is a 2-nilpotent Sylow tower Hall subgroup of G such that if x and y are G-conjugate elements of H ∩ G0 of prime order or order 4, then x and y are H-conjugate. We prove hat there exists a normal subgroup N of G such that G = HN and H ∩ N = 1.

2010 Mathematics Subject Classification: primary 20D20; secondary 20D10

Keywords: finite group, conjugation, Hall subgroup, normal complement.

Paper “On two questions from the Kourovka Notebook” published in J. Algebra

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A. Ballester-Bolinches, John Cossey, S. F. Kamornikov, H. Meng.

On two questions from the Kourovka Notebook

J. Algebra, 499:438-449, 2018

https://doi.org/10.1016/j.jalgebra.2017.12.014

Abstract

The aim of this paper is to give answers to some questions concerning intersections of system normalisers and prefrattini subgroups of finite soluble groups raised by the third author, Shemetkov and Vasil’ev in the Kourovka Notebook [10]. Our approach depends on results on regular orbits and it can be also used to extend a result of Mann [9] concerning intersections of injectors associated to Fitting classes.

2010 Mathematics Subject Classification: 20D10, 20D20

Keywords: Finite groups. Soluble groups. Formations. Fitting classes. Prefrattini  subgroups. Normalisers. Injectors.

Paper “Normalisers of residuals of finite groups” published in Arch. Math. (Basel)

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A. Ballester-Bolinches, S. F. Kamornikov, and H. Meng

Normalisers of residuals of finite groups

Arch. Math. (Basel), 109(4):305–310, 2017

https://doi.org/10.1007/s00013-017-1074-8

Abstract:

Let F be a subgroup-closed saturated formation of finite groups containing all finite nilpotent groups, and let M be a subgroup of a finite group G normalising the F-residual of every non-subnormal subgroup of G. We show that M normalises the F-residual of every subgroup of G. This answers a question posed by Gong and Isaacs (Arch Math 108:1–7, 2017) when F is the formation of all finite supersoluble groups.

2010 Mathematics Subject Classification: 20D10, 20D35

Keywords: Finite group, Formation, Residual, Subnormality