On a product of two formational tcc-subgroups
A subgroup A of a group G is called tcc-subgroup in G, if there is a subgroup T of G such that G = AT and for any X ≤ A and Y ≤ T there exists an element u ∈ hX, Y i such that XYᵘ ≤ G. The notation H ≤ G means that H is a subgroup of a group G. In this paper we consider a group G = AB such that A a...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2020 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/188571 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On a product of two formational tcc-subgroups / A. Trofimuk // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 2. — С. 282–289. — Бібліогр.: 15 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862697559919689728 |
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| author | Trofimuk, A. |
| author_facet | Trofimuk, A. |
| citation_txt | On a product of two formational tcc-subgroups / A. Trofimuk // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 2. — С. 282–289. — Бібліогр.: 15 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | A subgroup A of a group G is called tcc-subgroup in G, if there is a subgroup T of G such that G = AT and for any X ≤ A and Y ≤ T there exists an element u ∈ hX, Y i such that XYᵘ ≤ G. The notation H ≤ G means that H is a subgroup of a group G. In this paper we consider a group G = AB such that A and B are tcc-subgroups in G. We prove that G belongs to F, when A and B belong to F and F is a saturated formation of soluble groups such that U ⊆ F. Here U is the formation of all supersoluble groups.
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| first_indexed | 2025-12-07T16:30:05Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-188571 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T16:30:05Z |
| publishDate | 2020 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Trofimuk, A. 2023-03-06T14:58:51Z 2023-03-06T14:58:51Z 2020 On a product of two formational tcc-subgroups / A. Trofimuk // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 2. — С. 282–289. — Бібліогр.: 15 назв. — англ. 1726-3255 DOI:10.12958/adm1396 2010 MSC: 20D10. https://nasplib.isofts.kiev.ua/handle/123456789/188571 A subgroup A of a group G is called tcc-subgroup in G, if there is a subgroup T of G such that G = AT and for any X ≤ A and Y ≤ T there exists an element u ∈ hX, Y i such that XYᵘ ≤ G. The notation H ≤ G means that H is a subgroup of a group G. In this paper we consider a group G = AB such that A and B are tcc-subgroups in G. We prove that G belongs to F, when A and B belong to F and F is a saturated formation of soluble groups such that U ⊆ F. Here U is the formation of all supersoluble groups. For the 70th anniversary of L. A. Kurdachenko. This work was supported by the BRFFR (grant No. F19RM-071). en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On a product of two formational tcc-subgroups Article published earlier |
| spellingShingle | On a product of two formational tcc-subgroups Trofimuk, A. |
| title | On a product of two formational tcc-subgroups |
| title_full | On a product of two formational tcc-subgroups |
| title_fullStr | On a product of two formational tcc-subgroups |
| title_full_unstemmed | On a product of two formational tcc-subgroups |
| title_short | On a product of two formational tcc-subgroups |
| title_sort | on a product of two formational tcc-subgroups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188571 |
| work_keys_str_mv | AT trofimuka onaproductoftwoformationaltccsubgroups |