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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| Дата: | 2020 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2020
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/188571 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1885712023-03-07T01:26:58Z On a product of two formational tcc-subgroups Trofimuk, A. 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. 2020 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/188571 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Trofimuk, A. |
| spellingShingle |
Trofimuk, A. On a product of two formational tcc-subgroups Algebra and Discrete Mathematics |
| author_facet |
Trofimuk, A. |
| author_sort |
Trofimuk, A. |
| title |
On a product of two formational tcc-subgroups |
| title_short |
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_sort |
on a product of two formational tcc-subgroups |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2020 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/188571 |
| 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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT trofimuka onaproductoftwoformationaltccsubgroups |
| first_indexed |
2023-10-18T23:08:40Z |
| last_indexed |
2023-10-18T23:08:40Z |
| _version_ |
1796157362207195136 |