Let be some partition of the set of all primes, and let be a finite group. A chief factor of is said to be -central (in ) if the semidirect product is a -group for some ; otherwise, it is called -eccentric (in ). We say that is: -nilpotent if every chief factor of is -central; -quasinilpotent if for every -eccentric chief factor of , every automorphism of induced by an element of is inner. The product of all normal -nilpotent (respectively -quasinilpotent) subgroups of is said to be the -Fitting subgroup (respectively the generalized -Fitting subgroup) of and we denote it by (respectively by ). Our main goal here is to study the relations between the subgroups and , and the influence of these two subgroups on the structure of .
DOI : 10.4171/RSMUP/13
Mots-clés : Finite group, $\sigma$-nilpotent group, $\sigma$-quasinilpotent group, $\sigma$-Fitting subgroup, generalized $\sigma$-Fitting subgroup
@article{RSMUP_2019__141__19_0, 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/} }
TY - JOUR AU - Hu, Bin AU - Huang, Jianhong AU - Skiba, Alexander TI - On the generalized $\sigma$-Fitting subgroup of finite groups JO - Rendiconti del Seminario Matematico della Università di Padova PY - 2019 SP - 19 EP - 36 VL - 141 PB - European Mathematical Society Publishing House PP - Zuerich, Switzerland UR - http://www.numdam.org/articles/10.4171/RSMUP/13/ DO - 10.4171/RSMUP/13 ID - RSMUP_2019__141__19_0 ER -
%0 Journal Article %A Hu, Bin %A Huang, Jianhong %A Skiba, Alexander %T On the generalized $\sigma$-Fitting subgroup of finite groups %J Rendiconti del Seminario Matematico della Università di Padova %D 2019 %P 19-36 %V 141 %I European Mathematical Society Publishing House %C Zuerich, Switzerland %U http://www.numdam.org/articles/10.4171/RSMUP/13/ %R 10.4171/RSMUP/13 %F RSMUP_2019__141__19_0
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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