Title: | On the generalized σ-Fitting subgroup of finite groups |
Authors: | Hu, Bin Huang, Jianhong Skiba, A.N. Скиба, А.Н. |
Keywords: | finite group σ-nilpotent group σ-quasinilpotent group σ-Fitting subgroup generalized σ-Fitting subgroup |
Issue Date: | 2018 |
Citation: | Hu, B. On the generalized σ-Fitting subgroup of finite groups / Bin Hu, Jianhong Huang, A.N. Skiba // Rendiconti del Seminario Matematico della Università di Padova. – 2018. – Vol. 141. – P. 19-36. |
Abstract: | Let σ = {σi|i ∈ I} be some partition of the set ℙ 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) o (G/CG(H/K)) is a σi-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 Fσ(G) (respectively by Fσ*(G)). Our main goal here is to study the relations between the subgroups Fσ(G) and Fσ*(G), and the influence of these two subgroups on the structure of G. |
URI: | http://elib.gsu.by/jspui/handle/123456789/17633 |
Appears in Collections: | Статьи |
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