On the ℱ * -norm of a finite group
Rendiconti del Seminario Matematico della Università di Padova, Tome 145 (2021), pp. 181-190
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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 
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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},
     mrnumber = {4261652},
     zbl = {07367436},
     language = {en},
     url = {https://www.numdam.org/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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