On the -norm of a finite group

  • Quanfu Yan

    Kent State University, USA; Kent State University, USA
  • Zhencai Shen

    China Agricultural University, Beijing, China
On the $\mathcal{F}^*$-norm of a finite group cover

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Abstract

Let be a finite group and be a non-empty formation. We define the -norm, denoted by , to be intersection of the normalizers of the -residuals of all -subgroups of , where is the class of all groups whose -residuals are nilpotent. In this paper, we research the properties of and investigate the relationship between and where is the intersection of the normalizers of the -residuals of all subgroups of We show that if .

Cite this article

Quanfu Yan, Zhencai Shen, On the -norm of a finite group. Rend. Sem. Mat. Univ. Padova 145 (2021), pp. 181–190

DOI 10.4171/RSMUP/77