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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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2010 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2010
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/154605 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862633727027314688 |
|---|---|
| author | Dixon, M.R. Kurdachenko, L.A. Javier Otal |
| author_facet | Dixon, M.R. Kurdachenko, L.A. Javier Otal |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-11-30T15:32:18Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154605 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-30T15:32:18Z |
| publishDate | 2010 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Dixon, M.R. Kurdachenko, L.A. Javier Otal 2019-06-15T16:48:42Z 2019-06-15T16:48:42Z 2010 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 https://nasplib.isofts.kiev.ua/handle/123456789/154605 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. The second and third authors were supported by Proyecto MTM2010-19938-C03-03of Direcci ́on General de Investigaci ́on del MICINN (Spain) en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On the existence of complements in a group to some abelian normal subgroups Article published earlier |
| spellingShingle | On the existence of complements in a group to some abelian normal subgroups Dixon, M.R. Kurdachenko, L.A. Javier Otal |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154605 |
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