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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Veröffentlicht in:Algebra and Discrete Mathematics
Datum:2009
Hauptverfasser: Juriaans, O.S., Raphael, D.M.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут прикладної математики і механіки НАН України 2009
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/154638
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren: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
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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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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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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