On π𝔉-supplemented subgroups of a finite group
Rendiconti del Seminario Matematico della Università di Padova, Tome 136 (2016), pp. 175-189.

Let 𝔉 be a class of groups and G a finite group. A chief factor H/K of G is called 𝔉-central in G provided (H/K)(G/C G (H/K))𝔉. A normal subgroup N of G is said to be π𝔉-hypercentral in G if every chief factor of G below N of order divisible by at least one prime in π is 𝔉-central in G. The π𝔉-hypercentre of G is the product of all the normal π𝔉-hypercentral subgroups of G. In this paper, we study the structure of finite groups by using the notion of π𝔉-hypercentre. New characterizations of some classes of finite groups are obtained.

DOI : 10.4171/RSMUP/136-12
Classification : 20, 34
Mots clés : $\mathfrak{F}$-hypercentre, $\pi\mathfrak{F}$-hypercentre, Sylow subgroups, $n$-maximal subgroups
Zhang, Li 1 ; Chen, Xiaoyu 2 ; Guo, Wenbin 1

1 University of Scinece and Technology of China, HEFEI, CHINA
2 Nanjing Normal University, NANJING, CHINA
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     author = {Zhang, Li and Chen, Xiaoyu and Guo, Wenbin},
     title = {On $\pi\mathfrak{F}$-supplemented subgroups of a finite group},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {175--189},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {136},
     year = {2016},
     doi = {10.4171/RSMUP/136-12},
     url = {http://www.numdam.org/articles/10.4171/RSMUP/136-12/}
}
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Zhang, Li; Chen, Xiaoyu; Guo, Wenbin. On $\pi\mathfrak{F}$-supplemented subgroups of a finite group. Rendiconti del Seminario Matematico della Università di Padova, Tome 136 (2016), pp. 175-189. doi : 10.4171/RSMUP/136-12. http://www.numdam.org/articles/10.4171/RSMUP/136-12/

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