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 particular, we prove that a finite grou...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2005 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2005
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/157197 |
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| Zitieren: | 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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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Criterions of supersolubility of some finite factorizable groups |
| spellingShingle |
Criterions of supersolubility of some finite factorizable groups Legchekova, H.V. |
| title_short |
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_sort |
criterions of supersolubility of some finite factorizable groups |
| author |
Legchekova, H.V. |
| author_facet |
Legchekova, H.V. |
| publishDate |
2005 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/157197 |
| 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. |
| work_keys_str_mv |
AT legchekovahv criterionsofsupersolubilityofsomefinitefactorizablegroups |
| first_indexed |
2025-12-01T20:43:54Z |
| last_indexed |
2025-12-01T20:43:54Z |
| _version_ |
1850860922037338112 |