On the generalized σ-Fitting subgroup of finite groups
Rendiconti del Seminario Matematico della Università di Padova, Tome 141 (2019), pp. 19-36.
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Let σ={σ i |iI} be some partition of the set of all primes, and let G be a finite group. A chief factor H/K of G is said to be σ-central (in G) if the semidirect product (H/K)(G/C G (H/K)) is a σ i -group for some i=i(H/K); otherwise, it is called σ-eccentric (in G). We say that G is: σ-nilpotent if every chief factor of G is σ-central; σ-quasinilpotent if for every σ-eccentric chief factor H/K of G, every automorphism of H/K induced by an element of G is inner. The product of all normal σ-nilpotent (respectively σ-quasinilpotent) subgroups of G is said to be the σ-Fitting subgroup (respectively the generalized σ-Fitting subgroup) of G and we denote it by F σ (G) (respectively by F σ * (G)). Our main goal here is to study the relations between the subgroups F σ (G) and F σ * (G), and the influence of these two subgroups on the structure of G.

Publié le :
DOI : 10.4171/RSMUP/13
Classification : 13, 00
Mots clés : Finite group, $\sigma$-nilpotent group, $\sigma$-quasinilpotent group, $\sigma$-Fitting subgroup, generalized $\sigma$-Fitting subgroup
Hu, Bin 1 ; Huang, Jianhong 1 ; Skiba, Alexander 2

1 Jiangsu Normal University, Xuzhou, Jiangsu, China
2 Francisk Skorina Gomel State University, Belarus
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     author = {Hu, Bin and Huang, Jianhong and Skiba, Alexander},
     title = {On the generalized $\sigma${-Fitting} subgroup of finite groups},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {19--36},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {141},
     year = {2019},
     doi = {10.4171/RSMUP/13},
     mrnumber = {3962819},
     zbl = {1472.20028},
     url = {http://www.numdam.org/articles/10.4171/RSMUP/13/}
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Hu, Bin; Huang, Jianhong; Skiba, Alexander. On the generalized $\sigma$-Fitting subgroup of finite groups. Rendiconti del Seminario Matematico della Università di Padova, Tome 141 (2019), pp. 19-36. doi : 10.4171/RSMUP/13. http://www.numdam.org/articles/10.4171/RSMUP/13/

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