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 factors...
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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2009 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2009
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/154638 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | A new characterization of groups with central chief factors / O.S. Juriaans, D.M. Raphael // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 3. — С. 62–68. — Бібліогр.: 7 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862600029246586880 |
|---|---|
| author | Juriaans, O.S. Raphael, D.M. |
| author_facet | Juriaans, O.S. Raphael, D.M. |
| citation_txt | A new characterization of groups with central chief factors / O.S. Juriaans, D.M. Raphael // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 3. — С. 62–68. — Бібліогр.: 7 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-11-28T00:04:07Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154638 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-28T00:04:07Z |
| publishDate | 2009 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Juriaans, O.S. Raphael, D.M. 2019-06-15T17:03:58Z 2019-06-15T17:03:58Z 2009 A new characterization of groups with central chief factors / O.S. Juriaans, D.M. Raphael // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 3. — С. 62–68. — Бібліогр.: 7 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:Primary 2036, 16U70. Secondary20C10. https://nasplib.isofts.kiev.ua/handle/123456789/154638 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. Research partially supported by CNPq-Brazil. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics A new characterization of groups with central chief factors Article published earlier |
| spellingShingle | A new characterization of groups with central chief factors Juriaans, O.S. Raphael, D.M. |
| title | 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_short | A new characterization of groups with central chief factors |
| title_sort | new characterization of groups with central chief factors |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154638 |
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