Local Fitting sets and the injectors of a finite group

Authors

  • Tatyana B. Karaulova P. M. Masherov Vitebsk State University, 33 Maskoŭski Avenue, Vitebsk 210038, Belarus

Keywords:

Fitting set, F-injector, Hartley function, cover-avoid property
Supporting Agencies
Research is supported by the Belarusian Republican Foundation forFundamental Research (grant No. Ф17М-064).

Abstract

The product F  ◊  X of the Fitting set F of a group G and the Fitting class X is called the set of subgroups {H ≤ G: H/HF ∈ X}. Let P be the set of all primes, ∅ ≠ π ⊆ P, π′ = P\π and Eπ′ denote the class of all π′-groups. Let S and Sπ to denote the class of all soluble groups and the class of all π -soluble groups, respectively. In the paper, it is proved that F-injector of a group G either covers or avoids every chief factor of G if G is a partially soluble group. Chief factors of a group covered by F-injectors are described in the following cases: 1) G ∈ F  ◊  S and F  is the Hartley set of G; 2) G ∈ Sπ and F = F ◊ Eπ′ for the integrated H-function f.

Author Biography

  • Tatyana B. Karaulova, P. M. Masherov Vitebsk State University, 33 Maskoŭski Avenue, Vitebsk 210038, Belarus

    postgraduate student at the department  of algebra and methods of teaching mathematics, faculty of  mathematics and information technology

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Published

2019-01-19

Issue

No. 3 (2018): Journal of the Belarusian State University. Mathematics and Informatics

Section

Geometry and Algebra

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How to Cite

[1]
Karaulova, T.B. 2019. Local Fitting sets and the injectors of a finite group. Journal of the Belarusian State University. Mathematics and Informatics. 3 (Jan. 2019), 29–38.