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

Publié le :
DOI : 10.4171/rsmup/77
Classification : 20, 00
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     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/}
}
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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/

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