JournalsrsmupVol. 136pp. 175–189

On πF\pi\mathfrak{F}-supplemented subgroups of a finite group

  • Li Zhang

    University of Scinece and Technology of China, Hefei, China
  • Xiaoyu Chen

    Nanjing Normal University, China
  • Wenbin Guo

    University of Scinece and Technology of China, Hefei, China
On $\pi\mathfrak{F}$-supplemented subgroups of a finite group cover
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Abstract

Let F\mathfrak{F} be a class of groups and GG a finite group. A chief factor H/KH/K of GG is called F\mathfrak{F}-central in GG provided (H/K)(G/CG(H/K))F(H/K)\rtimes (G/C_{G}(H/K))\in\mathfrak{F}. A normal subgroup NN of GG is said to be πF\pi\mathfrak{F}-hypercentral in GG if every chief factor of GG below NN of order divisible by at least one prime in π\pi is F\mathfrak{F}-central in GG. The πF\pi\mathfrak{F}-hypercentre of GG is the product of all the normal πF\pi\mathfrak{F}-hypercentral subgroups of GG. In this paper, we study the structure of finite groups by using the notion of πF\pi\mathfrak{F}-hypercentre. New characterizations of some classes of finite groups are obtained.

Cite this article

Li Zhang, Xiaoyu Chen, Wenbin Guo, On πF\pi\mathfrak{F}-supplemented subgroups of a finite group. Rend. Sem. Mat. Univ. Padova 136 (2016), pp. 175–189

DOI 10.4171/RSMUP/136-12