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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| Date: | 2018 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/639 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | 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. |
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