A new characterization of groups with central chief factors
In [1] it is proved that a locally nilpotent group is an \((X)\)-group arising the question whether the converse holds. In this paper we derive some interesting properties and give a complete characterization of \((X)\)-groups. As a consequence we obtain a new characterization of groups whose chief...
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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/787 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | In [1] it is proved that a locally nilpotent group is an \((X)\)-group arising the question whether the converse holds. In this paper we derive some interesting properties and give a complete characterization of \((X)\)-groups. As a consequence we obtain a new characterization of groups whose chief factors are central and it follows also that there exists an \((X)\)-group which is not locally nilpotent, thus answering the question raised in [1]. We also prove a result which extends one on finitely generated nilpotent groups due to Gruenberg. |
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