On the ℱ * -norm of a finite group
Rendiconti del Seminario Matematico della Università di Padova, Tome 145 (2021), pp. 181-190.
Le texte intégral des articles récents est réservé aux abonnés de la revue. Consultez l'article sur le site de la revue.

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

Publié le :
DOI : 10.4171/rsmup/77
Classification : 20, 00 
@article{RSMUP_2021__145__181_0,
     author = {Quanfu Yan and Zhencai Shen},
     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  - Quanfu Yan
AU  - Zhencai Shen
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  - 
%0 Journal Article
%A Quanfu Yan
%A Zhencai Shen
%T On the $\mathcal{F}^*$-norm of a finite group
%J Rendiconti del Seminario Matematico della Università di Padova
%D 2021
%P 181-190
%V 145
%U http://www.numdam.org/articles/10.4171/rsmup/77/
%R 10.4171/rsmup/77
%G en
%F RSMUP_2021__145__181_0
Quanfu Yan; Zhencai Shen. 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/

Cité par Sources :