On verbal subgroups of finitely generated nilpotent groups

On verbal subgroups of finitely generated nilpotent groups

The paper concerns the problem of characterization of  verbal subgroups in finitely generated nilpotent groups. We introduce the notion of verbal poverty and show that every verbally poor finitely generated nilpotent group is a finite \(p\)-group with the lower \(p\)-central series for certain prime...

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Bibliographic Details
Date:2018
Main Author: Bier, Agnieszka
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2018
Subjects:
finitely generated nilpotent groups
verbal subgroups
20D15
20F18
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/773
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id oai:ojs.admjournal.luguniv.edu.ua:article-773
record_format ojs
spelling oai:ojs.admjournal.luguniv.edu.ua:article-7732018-04-04T08:38:30Z On verbal subgroups of finitely generated nilpotent groups Bier, Agnieszka finitely generated nilpotent groups, verbal subgroups 20D15, 20F18 The paper concerns the problem of characterization of  verbal subgroups in finitely generated nilpotent groups. We introduce the notion of verbal poverty and show that every verbally poor finitely generated nilpotent group is a finite \(p\)-group with the lower \(p\)-central series for certain prime \(p\). We conclude with few examples of verbally poor groups. 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/773 Algebra and Discrete Mathematics; Vol 8, No 2 (2009) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/773/303 Copyright (c) 2018 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2018-04-04T08:38:30Z
collection OJS
language English
topic finitely generated nilpotent groups
verbal subgroups
20D15
20F18
spellingShingle finitely generated nilpotent groups
verbal subgroups
20D15
20F18
Bier, Agnieszka
On verbal subgroups of finitely generated nilpotent groups
topic_facet finitely generated nilpotent groups
verbal subgroups
20D15
20F18
format Article
author Bier, Agnieszka
author_facet Bier, Agnieszka
author_sort Bier, Agnieszka
title On verbal subgroups of finitely generated nilpotent groups
title_short On verbal subgroups of finitely generated nilpotent groups
title_full On verbal subgroups of finitely generated nilpotent groups
title_fullStr On verbal subgroups of finitely generated nilpotent groups
title_full_unstemmed On verbal subgroups of finitely generated nilpotent groups
title_sort on verbal subgroups of finitely generated nilpotent groups
description The paper concerns the problem of characterization of  verbal subgroups in finitely generated nilpotent groups. We introduce the notion of verbal poverty and show that every verbally poor finitely generated nilpotent group is a finite \(p\)-group with the lower \(p\)-central series for certain prime \(p\). We conclude with few examples of verbally poor groups.
publisher Lugansk National Taras Shevchenko University
publishDate 2018
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/773
work_keys_str_mv AT bieragnieszka onverbalsubgroupsoffinitelygeneratednilpotentgroups
first_indexed 2025-07-17T10:37:19Z
last_indexed 2025-07-17T10:37:19Z
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