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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| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/787 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| id |
admjournalluguniveduua-article-787 |
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admjournalluguniveduua-article-7872018-04-04T08:43:10Z A new characterization of groups with central chief factors Juriaans, Orlando Stanley Raphael, Deborah Martins \((X)\)-group, nilpotent, residually central, Z-group Primary 2036, 16U70. Secondary 20C10 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. 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/787 Algebra and Discrete Mathematics; Vol 8, No 3 (2009) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/787/317 Copyright (c) 2018 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2018-04-04T08:43:10Z |
| collection |
OJS |
| language |
English |
| topic |
\((X)\)-group nilpotent residually central Z-group Primary 2036 16U70. Secondary 20C10 |
| spellingShingle |
\((X)\)-group nilpotent residually central Z-group Primary 2036 16U70. Secondary 20C10 Juriaans, Orlando Stanley Raphael, Deborah Martins A new characterization of groups with central chief factors |
| topic_facet |
\((X)\)-group nilpotent residually central Z-group Primary 2036 16U70. Secondary 20C10 |
| format |
Article |
| author |
Juriaans, Orlando Stanley Raphael, Deborah Martins |
| author_facet |
Juriaans, Orlando Stanley Raphael, Deborah Martins |
| author_sort |
Juriaans, Orlando Stanley |
| title |
A new characterization of groups with central chief factors |
| title_short |
A new characterization of groups with central chief factors |
| title_full |
A new characterization of groups with central chief factors |
| title_fullStr |
A new characterization of groups with central chief factors |
| title_full_unstemmed |
A new characterization of groups with central chief factors |
| title_sort |
new characterization of groups with central chief factors |
| description |
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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/787 |
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AT juriaansorlandostanley anewcharacterizationofgroupswithcentralchieffactors AT raphaeldeborahmartins anewcharacterizationofgroupswithcentralchieffactors AT juriaansorlandostanley newcharacterizationofgroupswithcentralchieffactors AT raphaeldeborahmartins newcharacterizationofgroupswithcentralchieffactors |
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2025-12-02T15:37:03Z |
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2025-12-02T15:37:03Z |
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1850411396147183617 |