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. 181–190DOI 10.4171/RSMUP/77