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https://rep.vsu.by/handle/123456789/33410
Title: | On σ-local Fitting classes |
Authors: | Guo, Wenbin Zhang, Li Vorob'ev, N.T. |
Keywords: | Finite group Fitting class Hartley σ-function Lockett class σ-local Fitting class |
Issue Date: | Jan-2020 |
Publisher: | Elsevier |
Citation: | Guo, W. On σ-local Fitting classes / Guo, W., Zhang, L. & Vorob`ev, N. T. // Journal of Algebra. – 2020. – Vol. 542. – P. 116–129. |
Series/Report no.: | Journal of Algebra;Vol. 542 |
Abstract: | Let σ be a partition of the set of all primes P. If G is a finite group and F is a Fitting class of finite groups, the symbol σ(G) denotes the set {σi|σi∩π(|G|)≠∅} and σ(F)=∪σ∈Fσ(G). We call any function f of the form f:σ⟶{Fitting classes} a Hartley σ-function (or simply Hσ-function), and we put LRσ(f)=(G|G=1orG≠1andGG∈f(σi)for allσi∈σ(G)). If there is an Hσ-function f such that F=LRσ(f), then we say that F is σ-local and f is a σ-local definition of F. In this paper, we describe some properties of σ-local Fitting classes and prove that: 1) every σ-local Fitting class can be defined by a unique Hσ-function F such that F(σi)=F(σi)Gσ⊆F and F(σi) is a Lockett class for all σi∈σ(F); 2) the product of two σ-local Fitting classes is also a σ-local Fitting class. Moreover, we also discuss the n-multiply σ-local Fitting classes. |
URI: | https://rep.vsu.by/handle/123456789/33410 |
ISSN: | 0021-8693 |
Appears in Collections: | Научные публикации (2020) |
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Journal of Algebra_2020_ Vol. 542.pdf | 395.58 kB | Adobe PDF | View/Open |
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