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 p. We c...
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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2009 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2009
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/154508 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On verbal subgroups of finitely generated nilpotent groups / A. Bier // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 2. — С. 1–10. — Бібліогр.: 5 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862530629579571200 |
|---|---|
| author | Bier, A. |
| author_facet | Bier, A. |
| citation_txt | On verbal subgroups of finitely generated nilpotent groups / A. Bier // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 2. — С. 1–10. — Бібліогр.: 5 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-11-24T02:42:09Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154508 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-24T02:42:09Z |
| publishDate | 2009 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Bier, A. 2019-06-15T16:21:28Z 2019-06-15T16:21:28Z 2009 On verbal subgroups of finitely generated nilpotent groups / A. Bier // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 2. — С. 1–10. — Бібліогр.: 5 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:20D15, 20F18.. https://nasplib.isofts.kiev.ua/handle/123456789/154508 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On verbal subgroups of finitely generated nilpotent groups Article published earlier |
| spellingShingle | On verbal subgroups of finitely generated nilpotent groups Bier, A. |
| title | 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_short | On verbal subgroups of finitely generated nilpotent groups |
| title_sort | on verbal subgroups of finitely generated nilpotent groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154508 |
| work_keys_str_mv | AT biera onverbalsubgroupsoffinitelygeneratednilpotentgroups |