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 .
@article{RSMUP_2021__145__181_0, 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}, volume = {145}, year = {2021}, doi = {10.4171/rsmup/77}, mrnumber = {4261652}, zbl = {07367436}, language = {en}, url = {http://www.numdam.org/articles/10.4171/rsmup/77/} }
TY - JOUR AU - Yan, Quanfu AU - Shen, Zhencai TI - On the $\mathcal{F}^*$-norm of a finite group JO - Rendiconti del Seminario Matematico della Università di Padova PY - 2021 SP - 181 EP - 190 VL - 145 UR - http://www.numdam.org/articles/10.4171/rsmup/77/ DO - 10.4171/rsmup/77 LA - en ID - RSMUP_2021__145__181_0 ER -
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. http://www.numdam.org/articles/10.4171/rsmup/77/
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