On the generalized -Fitting subgroup of finite groups

  • Bin Hu

    Jiangsu Normal University, Xuzhou, Jiangsu, China
  • Jianhong Huang

    Jiangsu Normal University, Xuzhou, Jiangsu, China
  • Alexander N. Skiba

    Francisk Skorina Gomel State University, Belarus
On the generalized $\sigma$-Fitting subgroup of finite groups cover
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Abstract

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. 19–36

DOI 10.4171/RSMUP/13