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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| Sprache: | English |
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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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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 |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2018-04-04T09:14:15Z |
| collection |
OJS |
| language |
English |
| topic |
Complement splitting theorem hierarchy of centralizers hyperfinite group socle of a group socular series section rank 0–rank 20E22 20E26 20F50 |
| 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 |
| topic_facet |
Complement splitting theorem hierarchy of centralizers hyperfinite group socle of a group socular series section rank 0–rank 20E22 20E26 20F50 |
| format |
Article |
| author |
Dixon, Martyn R. Kurdachenko, Leonid A. Otal, Javier |
| author_facet |
Dixon, Martyn R. Kurdachenko, Leonid A. Otal, Javier |
| author_sort |
Dixon, Martyn 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 |
| 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| 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 |
| first_indexed |
2025-12-02T15:31:52Z |
| last_indexed |
2025-12-02T15:31:52Z |
| _version_ |
1850412081679958016 |