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 \(H\cap K=\langle1\rangle\). 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...
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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/639 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543260710797312 |
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| author | Dixon, Martyn R. Kurdachenko, Leonid A. Otal, Javier |
| author_facet | Dixon, Martyn R. Kurdachenko, Leonid A. Otal, Javier |
| author_sort | Dixon, Martyn R. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-04T09:14:15Z |
| description | A complement to a proper normal subgroup \(H\) of a group \(G\) is a subgroup \(K\) such that \(G=HK\) and \(H\cap K=\langle1\rangle\). 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. |
| first_indexed | 2025-12-02T15:31:52Z |
| format | Article |
| id | admjournalluguniveduua-article-639 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:31:52Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-6392018-04-04T09:14:15Z On the existence of complements in a group to some abelian normal subgroups Dixon, Martyn R. Kurdachenko, Leonid A. Otal, Javier Complement, splitting theorem, hierarchy of centralizers, hyperfinite group, socle of a group, socular series, section rank, 0–rank 20E22, 20E26, 20F50 A complement to a proper normal subgroup \(H\) of a group \(G\) is a subgroup \(K\) such that \(G=HK\) and \(H\cap K=\langle1\rangle\). 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. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/639 Algebra and Discrete Mathematics; Vol 10, No 1 (2010) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/639/173 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | Complement splitting theorem hierarchy of centralizers hyperfinite group socle of a group socular series section rank 0–rank 20E22 20E26 20F50 Dixon, Martyn R. Kurdachenko, Leonid A. Otal, Javier On the existence of complements in a group to some abelian normal subgroups |
| 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 |
| topic | Complement splitting theorem hierarchy of centralizers hyperfinite group socle of a group socular series section rank 0–rank 20E22 20E26 20F50 |
| topic_facet | Complement splitting theorem hierarchy of centralizers hyperfinite group socle of a group socular series section rank 0–rank 20E22 20E26 20F50 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/639 |
| work_keys_str_mv | AT dixonmartynr ontheexistenceofcomplementsinagrouptosomeabeliannormalsubgroups AT kurdachenkoleonida ontheexistenceofcomplementsinagrouptosomeabeliannormalsubgroups AT otaljavier ontheexistenceofcomplementsinagrouptosomeabeliannormalsubgroups |