On verbal subgroups in finite and profinite groups
Let w be a multilinear commutator word. In the present paper we describe recent results that show that if G is a profinite group in which all w-values are contained in a union of finitely (or in some cases countably) many subgroups with a prescribed property, then the verbal subgroup w(G) has the sa...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
|---|---|
| Datum: | 2012 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2012
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/152224 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On verbal subgroups in finite and profinite groups / C. Acciarri, P. Shumyatsky // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 1. — С. 1–13. — Бібліогр.: 32 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862690611819184128 |
|---|---|
| author | Acciarri, C. Shumyatsky, P. |
| author_facet | Acciarri, C. Shumyatsky, P. |
| citation_txt | On verbal subgroups in finite and profinite groups / C. Acciarri, P. Shumyatsky // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 1. — С. 1–13. — Бібліогр.: 32 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | Let w be a multilinear commutator word. In the present paper we describe recent results that show that if G is a profinite group in which all w-values are contained in a union of finitely (or in some cases countably) many subgroups with a prescribed property, then the verbal subgroup w(G) has the same property as well. In particular, we show this in the case where the subgroups are periodic or of finite rank.
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| first_indexed | 2025-12-07T16:13:52Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-152224 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T16:13:52Z |
| publishDate | 2012 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Acciarri, C. Shumyatsky, P. 2019-06-09T05:35:05Z 2019-06-09T05:35:05Z 2012 On verbal subgroups in finite and profinite groups / C. Acciarri, P. Shumyatsky // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 1. — С. 1–13. — Бібліогр.: 32 назв. — англ. 1726-3255 2010 MSC:Primary 20E18; Secondary 20F14. https://nasplib.isofts.kiev.ua/handle/123456789/152224 Let w be a multilinear commutator word. In the present paper we describe recent results that show that if G is a profinite group in which all w-values are contained in a union of finitely (or in some cases countably) many subgroups with a prescribed property, then the verbal subgroup w(G) has the same property as well. In particular, we show this in the case where the subgroups are periodic or of finite rank. This research was supported by CNPq-Brazil. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On verbal subgroups in finite and profinite groups Article published earlier |
| spellingShingle | On verbal subgroups in finite and profinite groups Acciarri, C. Shumyatsky, P. |
| title | On verbal subgroups in finite and profinite groups |
| title_full | On verbal subgroups in finite and profinite groups |
| title_fullStr | On verbal subgroups in finite and profinite groups |
| title_full_unstemmed | On verbal subgroups in finite and profinite groups |
| title_short | On verbal subgroups in finite and profinite groups |
| title_sort | on verbal subgroups in finite and profinite groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152224 |
| work_keys_str_mv | AT acciarric onverbalsubgroupsinfiniteandprofinitegroups AT shumyatskyp onverbalsubgroupsinfiniteandprofinitegroups |