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 .
Cite this article
Bin Hu, Jianhong Huang, Alexander N. Skiba, On the generalized -Fitting subgroup of finite groups. Rend. Sem. Mat. Univ. Padova 141 (2019), pp. 19–36DOI 10.4171/RSMUP/13