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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Опубліковано в: :Algebra and Discrete Mathematics
Дата:2005
Автор: Legchekova, H.V.
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут прикладної математики і механіки НАН України 2005
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/157197
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати: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
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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
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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