On the existence of complements in a group to some abelian normal subgroups
A complement to a proper normal subgroup H of a group G is a subgroup K such that G=HK and H∩K=⟨1⟩. Equivalently it is said that G splits over H. In this paper we develop a theory that we call hierarchy of centralizers to obtain sufficient conditions for a group to split over a certain abelian subgr...
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| Дата: | 2010 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2010
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/154605 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On the existence of complements in a group to some abelian normal subgroups / M.R. Dixon, L.A. Kurdachenko, Javier Otal // Algebra and Discrete Mathematics. — 2010. — Vol. 10, № 1. — С. 18–41. — Бібліогр.: 32 назв. — англ. |
Репозитарії
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irk-123456789-154605 |
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irk-123456789-1546052019-06-16T01:32:04Z On the existence of complements in a group to some abelian normal subgroups Dixon, M.R. Kurdachenko, L.A. Javier Otal A complement to a proper normal subgroup H of a group G is a subgroup K such that G=HK and H∩K=⟨1⟩. Equivalently it is said that G splits over H. In this paper we develop a theory that we call hierarchy of centralizers to obtain sufficient conditions for a group to split over a certain abelian subgroup. We apply these results to obtain an entire group-theoretical wide extension of an important result due to D. J. S. Robinson formerly shown by cohomological methods. 2010 Article On the existence of complements in a group to some abelian normal subgroups / M.R. Dixon, L.A. Kurdachenko, Javier Otal // Algebra and Discrete Mathematics. — 2010. — Vol. 10, № 1. — С. 18–41. — Бібліогр.: 32 назв. — англ. 1726-3255 2010 Mathematics Subject Classification:20E22, 20E26, 20F50 http://dspace.nbuv.gov.ua/handle/123456789/154605 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 complement to a proper normal subgroup H of a group G is a subgroup K such that G=HK and H∩K=⟨1⟩. Equivalently it is said that G splits over H. In this paper we develop a theory that we call hierarchy of centralizers to obtain sufficient conditions for a group to split over a certain abelian subgroup. We apply these results to obtain an entire group-theoretical wide extension of an important result due to D. J. S. Robinson formerly shown by cohomological methods. |
| format |
Article |
| author |
Dixon, M.R. Kurdachenko, L.A. Javier Otal |
| spellingShingle |
Dixon, M.R. Kurdachenko, L.A. Javier Otal On the existence of complements in a group to some abelian normal subgroups Algebra and Discrete Mathematics |
| author_facet |
Dixon, M.R. Kurdachenko, L.A. Javier Otal |
| author_sort |
Dixon, M.R. |
| title |
On the existence of complements in a group to some abelian normal subgroups |
| title_short |
On the existence of complements in a group to some abelian normal subgroups |
| title_full |
On the existence of complements in a group to some abelian normal subgroups |
| title_fullStr |
On the existence of complements in a group to some abelian normal subgroups |
| title_full_unstemmed |
On the existence of complements in a group to some abelian normal subgroups |
| title_sort |
on the existence of complements in a group to some abelian normal subgroups |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/154605 |
| citation_txt |
On the existence of complements in a group to some abelian normal subgroups / M.R. Dixon, L.A. Kurdachenko, Javier Otal // Algebra and Discrete Mathematics. — 2010. — Vol. 10, № 1. — С. 18–41. — Бібліогр.: 32 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
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| first_indexed |
2023-05-20T17:44:58Z |
| last_indexed |
2023-05-20T17:44:58Z |
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1796153999867510784 |