On the -norm of a finite group
Rendiconti del Seminario Matematico della Università di Padova, Tome 145 (2021), pp. 181-190
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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 .
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author = {Yan, Quanfu and Shen, Zhencai},
title = {On the $\mathcal{F}^*$-norm of a finite group},
journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
pages = {181--190},
year = {2021},
volume = {145},
doi = {10.4171/rsmup/77},
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language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4171/rsmup/77/}
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Yan, Quanfu; Shen, Zhencai. On the $\mathcal{F}^*$-norm of a finite group. Rendiconti del Seminario Matematico della Università di Padova, Tome 145 (2021), pp. 181-190. doi: 10.4171/rsmup/77
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