Local Fitting sets and the injectors of a finite group
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...
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| Format: | Article |
| Language: | Belarusian |
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Belarusian State University
2019-01-01
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| Series: | Журнал Белорусского государственного университета: Математика, информатика |
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| Online Access: | https://journals.bsu.by/index.php/mathematics/article/view/1010 |
| Summary: | 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. |
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| ISSN: | 2520-6508 2617-3956 |