Criterions of supersolubility of some finite factorizable groups
Let A, B be subgroups of a group G and ∅ 6= X ⊆
 G. A subgroup A is said to be X-permutable with B if for some
 x ∈ X we have ABx = BxA [1]. We obtain some new criterions
 for supersolubility of a finite group G = AB, where A and B are
 supersoluble groups. In particu...
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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2005 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2005
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/157197 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Criterions of supersolubility of some finite factorizable groups / H.V. Legchekova // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 3. — С. 46–55. — Бібліогр.: 16 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862651771312144384 |
|---|---|
| author | Legchekova, H.V. |
| author_facet | Legchekova, H.V. |
| citation_txt | Criterions of supersolubility of some finite factorizable groups / H.V. Legchekova // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 3. — С. 46–55. — Бібліогр.: 16 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | Let A, B be subgroups of a group G and ∅ 6= X ⊆
G. A subgroup A is said to be X-permutable with B if for some
x ∈ X we have ABx = BxA [1]. We obtain some new criterions
for supersolubility of a finite group G = AB, where A and B are
supersoluble groups. In particular, we prove that a finite group
G = AB is supersoluble provided A, B are supersolube subgroups
of G such that every primary cyclic subgroup of A X-permutes with
every Sylow subgroup of B and if in return every primary cyclic
subgroup of B X-permutes with every Sylow subgroup of A where
X = F(G) is the Fitting subgroup of G.
|
| first_indexed | 2025-12-01T20:43:54Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-157197 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-01T20:43:54Z |
| publishDate | 2005 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Legchekova, H.V. 2019-06-19T17:31:49Z 2019-06-19T17:31:49Z 2005 Criterions of supersolubility of some finite factorizable groups / H.V. Legchekova // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 3. — С. 46–55. — Бібліогр.: 16 назв. — англ. 1726-3255 2000 Mathematics Subject Classification: 20D20. https://nasplib.isofts.kiev.ua/handle/123456789/157197 Let A, B be subgroups of a group G and ∅ 6= X ⊆
 G. A subgroup A is said to be X-permutable with B if for some
 x ∈ X we have ABx = BxA [1]. We obtain some new criterions
 for supersolubility of a finite group G = AB, where A and B are
 supersoluble groups. In particular, we prove that a finite group
 G = AB is supersoluble provided A, B are supersolube subgroups
 of G such that every primary cyclic subgroup of A X-permutes with
 every Sylow subgroup of B and if in return every primary cyclic
 subgroup of B X-permutes with every Sylow subgroup of A where
 X = F(G) is the Fitting subgroup of G. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Criterions of supersolubility of some finite factorizable groups Article published earlier |
| spellingShingle | Criterions of supersolubility of some finite factorizable groups Legchekova, H.V. |
| title | Criterions of supersolubility of some finite factorizable groups |
| title_full | Criterions of supersolubility of some finite factorizable groups |
| title_fullStr | Criterions of supersolubility of some finite factorizable groups |
| title_full_unstemmed | Criterions of supersolubility of some finite factorizable groups |
| title_short | Criterions of supersolubility of some finite factorizable groups |
| title_sort | criterions of supersolubility of some finite factorizable groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/157197 |
| work_keys_str_mv | AT legchekovahv criterionsofsupersolubilityofsomefinitefactorizablegroups |